Practice: Series Circuits

Question 1

In a series circuit, certain general rules may be stated with regard to quantities of voltage, current, resistance, and power. Express these rules, using your own words:

"In a series circuit, voltage . . ."

"In a series circuit, current . . ."

"In a series circuit, resistance . . ."

"In a series circuit, power . . ."

For each of these rules, explain why it is true.

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Question 2

Identify which of these circuits is a series circuit (there may be more than one shown!):

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Question 3

Draw connecting wires that will create a series circuit, such that voltage will drop across each resistor in the polarity shown by the (+) and (\(-\)) symbols:

Suggestions for Socratic discussion

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Question 4

Qualitatively compare the voltage and current for each of the three light bulbs in this circuit (assume the three light bulbs are absolutely identical):

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Question 5

What would happen if three 6-volt light bulbs were connected as shown to a 6-volt battery? How would their brightnesses compare to just having a single 6-volt light bulb connected to a 6-volt battery?

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Question 6

What will happen in this circuit as the switches are sequentially turned on, starting with switch number 1 and ending with switch number 3?

Describe how the successive closure of these three switches will impact:

Also, provide a safety-related reason for the existence of the fourth resistor in this circuit, on the left-hand side of the circuit (not bypassed by any switch).

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Question 7

Determine both the polarity of voltage across the resistor in this circuit, and how much voltage will be dropped across the resistor:

Explain the procedure(s) you used to answer both these questions.

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Question 8

Suppose a voltmeter has a range of 0 to 10 volts, and an internal resistance of 100 k\(\Omega\):

Show how a single resistor could be connected to this voltmeter to extend its range to 0 to 50 volts. Calculate the resistance of this "range" resistor, as well as its necessary power dissipation rating.

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Question 9

What size (gauge) of copper wire is needed in this circuit to ensure the load receives at least 110 volts?

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Question 10

Use Kirchhoff’s Voltage Law to calculate the magnitude and polarity of the voltage across resistor \(R_4\) in this resistor network:

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Question 11

Suppose you wanted to measure the amount of current going through resistor R2 on this printed circuit board, but did not have the luxury of breaking the circuit to do so (unsoldering one end of the resistor, detaching it from the PCB, and connecting an ammeter in series). All you can do while the circuit is powered is measure voltage with a voltmeter:

So, you decide to touch the black probe of the voltmeter to the circuit’s "Gnd" (ground) test point, and measure the voltage with reference to ground on both sides of R2. The results are shown here:

R2’s color code is Orange, Orange, Red, Gold. Based on this information, determine both the direction and the magnitude of DC current through resistor R2, and explain how you did so.

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Question 12

Imagine you are using a digital voltmeter to measure voltages between pairs of points in a circuit, following the sequence of steps shown in these diagrams:

How much voltage would be registered by the voltmeter in each of the steps? Be sure to include the sign of the DC voltage measured (note the coloring of the voltmeter leads, with the red lead always on the first point denoted in the subscript: \(V_{BA}\) = red lead on "B" and black lead on "A"):

What is the algebraic sum of these voltages?

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Question 13

Determine what the magnitude and polarity of the voltmeter’s indication will be in each case:

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Question 14

How much voltage does the light bulb receive in this circuit? Explain your answer.

Also, identify the polarity of the voltage across the light bulb (mark with "+" and "-" signs).

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Question 15

Identify each of the specified voltages in the following circuit. The subscripts refer to the specific test points (where the red test lead of the voltmeter touches the circuit), while ground is the point where the voltmeter’s black lead is assumed to be attached:

For example, \(V_B\) means the voltage indicated by a voltmeter with the red test lead touching point B and the black test lead touching ground.

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Question 16

Complete the table of values for this circuit:

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Question 17

Determine what will happen to all voltage drops in this circuit if the resistance of resistor \(R_3\) happens to increase:

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Question 18

Predict how all test point voltages (measured between each test point and ground) in this circuit will be affected as a result of the following faults. Consider each fault independently (i.e. one at a time, no multiple faults):

For each of these conditions, explain why the resulting effects will occur.

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Question 19

What hazards might be posed by a circuit with excessive current going through its conductors (excessive as defined by the conductors’ ampacity)? In other words, what would be bad about a wire carrying too much current?

Also determine which type of component fault, an open or a short, would most likely be the cause of excessive current in a circuit.

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Question 20

What is the difference between a fuse and a circuit breaker?

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Question 21

Are fuses and circuit breakers located at a power distribution panel rated to protect the wiring from overcurrent, or to protect the load devices from overcurrent? Explain your answer.

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Question 22

A large industrial electric motor is supplied power through a pair of fuses:

One day the motor suddenly stops running, even though the switch is still in the "on" position. An electrician is summoned to troubleshoot the failed motor, and this person decides to perform some voltage measurements to determine whether or not one of the fuses has "blown" open before doing anything else. The measurements taken by the electrician are as such (with the switch in the "on" position):

Based on these measurements, the electrician decides that both fuses are still in good condition, and that the problem lies elsewhere in the circuit. Do you agree with this assessment? Why or why not?

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Question 23

Is there any shock hazard posed to a person touching the metal case of this appliance? Explain your answer.

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Question 24

The metal case of this appliance is grounded by means of a third conductor:

Explain how this grounding connection makes the appliance safer for anyone touching its metal case.

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Question 25

The presence of a "ground" wire increases the degree of electrical safety for anyone using an electrical appliance. It entails having a third "prong" on the power plug, connecting with a third hole on the power receptacle, which connects to a separate wire running all the way back to the power system’s grounding point:

But why not eliminate all that extra wiring, and simply connect the third hole on the power receptacle to the "neutral" wire?

Why would this idea be unwise?

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Question 26

Question 27

Suppose that an electric heater, which is nothing more than a large resistor, dissipates 500 watts of power when directly connected to a 110 volt source:

Now suppose that exact same heater is connected to one end of a long two-wire cable, which is then connected to the same 110 volt source. Assuming that each conductor within the cable has an end-to-end resistance of 3 ohms, how much power will the heater dissipate?

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Question 28

Question 29

Show the proper placement of the fuse in this circuit, where an electric motor will be powered by utility (120 volt AC) power:

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Question 30

Calculate \(V_A\) (voltage at point A with respect to ground) and \(V_B\) (voltage at point B with respect to ground) in the following circuit:

Now, calculate the voltage between points A and B (\(V_{AB}\)).

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Question 31

Shown here is a simple telegraph circuit:

Explain why the lamps energize when either pushbutton is actuated, and why they de-energize when both pushbuttons are open (despite there being an unbroken circuit connecting both lamps and both batteries).

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Question 32

Draw a schematic diagram showing a potentiometer being used as a simple variable resistor for varying current to a light bulb. Also, designate which way the "wiper" should be moved to make the bulb glow brighter.

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Question 33

Examine the following illustration of a simple battery-switch-lamp circuit, connected together using screw-terminal blocks, each connection point on each terminal block identified by a unique number:

Determine whether or not voltage should be present between the following pairs of terminal block points with the switch in the ON position:

Now, determine whether or not voltage should be present between the following pairs of terminal block points with the switch in the OFF position:

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Question 34

Design a voltage divider circuit that splits the power supply voltage into the following percentages:

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Question 35

Determine the amount of voltage dropped by each resistor in this circuit, if each resistor has a color code of Brn, Blk, Red, Gld (assume perfectly precise resistance values – 0/ error):

Also, determine the following information about this circuit:

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Question 36

The circuit shown here is called a "bridge rectifier," and its purpose is to convert alternating current (from the "power-supply" unit) into direct current. Suppose you were instructed to check the continuity of the switch (SW1) mounted on the printed circuit board. What would be a fast and effective way of testing this switch’s continuity (ideally, without removing the switch from the circuit board)?

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Question 37

How much voltage does the light bulb receive in this circuit? Explain your answer.

Also, identify the polarity of the voltage across the light bulb (mark with "+" and "-" signs).

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Question 38

Most flashlights use multiple 1.5 volt batteries to power a light bulb with a voltage rating of several volts. Draw a schematic diagram of showing how multiple batteries may be connected to achieve a total voltage greater than any one of the batteries’ individual voltages.

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Question 39

Explain, step by step, how to calculate the amount of current (\(I\)) that will go through each resistor in this series circuit, and also the voltage (\(V\)) dropped by each resistor:

Use the procedure that you created to find the current through and voltage across each resistor.

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Question 40

Calculate the amount of voltage between test points TP1 and TP3, and also the amount of voltage between test points TP2 and TP4:

\(V_{TP1-TP3}\) = \(V_{TP2-TP4}\) =

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Question 41

Calculate the voltage dropped by each of these resistors, given a battery voltage of 9 volts. The resistor color codes are as follows (assume 0/ error on all resistor values):

\(R_1 =\) Brn, Grn, Red, Gld

\(R_2 =\) Yel, Vio, Org, Gld

\(R_3 =\) Red, Grn, Red, Gld

\(R_4 =\) Wht, Blk, Red, Gld

Now, re-calculate all resistor voltage drops for a scenario where the total voltage is different:

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Question 42

Explain the construction and purpose of an electrical fuse.

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Question 43

Determine the polarity of voltage across the resistor in this simple circuit, and be prepared to explain how you did so:

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Question 44

Imagine you are using a digital voltmeter to measure voltages between pairs of points in a circuit, following the sequence of steps shown in these diagrams:

How much voltage would be registered by the voltmeter in each of the steps? Be sure to include the sign of the DC voltage measured (note the coloring of the voltmeter leads, with the red lead always on the first point denoted in the subscript: \(V_{BA}\) = red lead on "B" and black lead on "A"):

Challenge question: how do these voltage measurements prove Kirchhoff’s Voltage Law, where the algebraic sum of all voltages in a loop equals 0 volts?

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Question 45

Calculate the output voltages of these two voltage divider circuits (\(V_A\) and \(V_B\)):

Now, calculate the voltage between points A (red lead) and B (black lead) (\(V_{AB}\)).

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Question 46

Draw connecting wires that will create a series circuit, such that current (conventional flow notation) will follow the directions shown by the arrows near each resistor:

Suggestions for Socratic discussion

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Question 47

The formula for calculating voltage across a resistor in a series circuit is as follows:

In a simple-series circuit with one voltage source and three resistors, we may re-write this formula to be more specific:

Suppose we have such a series circuit with a source voltage of 15 volts, and resistor values of \(R_1\) = 1 k\(\Omega\) and \(R_2\) = 8.1 k\(\Omega\). Algebraically manipulate this formula to solve for \(R_3\) in terms of all the other variables, then determine the necessary resistance value of \(R_3\) to obtain a 0.2 volt drop across resistor \(R_1\).

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Question 48

Draw connecting wires that will create a series circuit with all the components shown:

Suggestions for Socratic discussion

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Question 49

Draw connecting wires that will create a series circuit, such that current (conventional flow notation) will follow the directions shown by the arrows near each resistor:

Suggestions for Socratic discussion

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Question 50

A technician wants to energize a 24 volt motor, but lacks a 24 volt battery to do it with. Instead, she has access to several "power supply" units which convert 120 volt AC power from a power receptacle into low-voltage DC power that is adjustable over a range of 0 to 15 volts. Each of these power supplies is a box with a power cord, voltage adjustment knob, and two output terminals for connection with the DC voltage it produces:

Draw a picture of how this technician might use power supplies to energize the 24 volt motor.

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Question 51

How much voltage does the light bulb receive in this circuit? Explain your answer.

Also, identify the polarity of the voltage across the light bulb (mark with "+" and "-" signs).

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Question 52

Determine what a digital voltmeter (DVM) would indicate if connected between the following points in this circuit:

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Question 53

Determine what a digital voltmeter (DVM) would indicate if connected between the following points in this circuit:

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Question 54

The following circuit has a problem. When the switch is closed, the lamp does not turn on:

Identify which of these hypothetical faults could account for this problem, and which could not account for the problem. In other words, which of these faults are possible, and which are not possible, given the symptoms exhibited by the circuit? Consider each of these hypothetical faults one at a time (no multiple, simultaneous faults):

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Question 55

The circuit shown here is commonly referred to as a voltage divider. Calculate the voltage dropped across the following pairs of terminals, the current through each resistor, and the total amount of electrical resistance "seen" by the 9-volt battery:

Can you think of any practical applications for a circuit such as this?

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Question 56

Design a voltage divider circuit that splits the power supply voltage into the following percentages:

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Question 57

Determine what these two voltmeters will register with the circuit grounded at three different points (each grounding scenario considered one at a time, not simultaneously). Note that neither voltmeter moves, nor are any of their test leads moved, between scenarios. The only difference is where we connect earth ground to the circuit:

Suggestions for Socratic discussion

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Answer 1

"In a series circuit, voltage drops add to equal the total."

"In a series circuit, current is equal through all components."

"In a series circuit, resistance_s add to equal the total_."

"In a series circuit, power dissipations add to equal the total."

Answer 2

Circuits A, C, and F are series circuits.

Answer 3

Bear in mind that this is not the only possible circuit solution:

Challenge yourself by designing a different circuit to meet the same criteria!

Answer 4

The current through each of the lights bulbs is guaranteed to be equal. The voltage across each of the light bulbs, in this particular case (with identical bulbs), happens to be equal.

Answer 5

The three light bulbs would glow dimly.

Answer 6

I won’t explain what happens when each of the switches is closed, but I will describe the effects of the first switch closing:

As the first switch (SW1) is closed, the voltage across resistor R1 will decrease to zero, while the voltages across the remaining resistors will increase. The current through resistor R1 will also decrease to zero, and the current through the remaining resistors will also increase. Each of the resistors will experience the same amount of current as the others, and this amount of current will also be experienced by the battery. Overall, the battery "sees" less total resistance than before.

The fourth resistor is there to prevent a short-circuit from developing if all switches are simultaneously closed.

Answer 7

Answer 8

A power dissipation rating of \({1 \over 8}\) watt would be more than sufficient for this application.

Answer 9

#6 gauge copper wire comes close, but is not quite large enough. #5 gauge or larger will suffice.

Answer 10

Answer 11

\(I_{R2} \approx 160 \> \mu {A}\), conventional flow from left to right (electron flow from right to left).

Follow-up question: this technique for estimating resistor current depends on one important assumption. Describe what this assumption is, and how the accuracy of your current calculation may be affected if the assumption is invalid.

Answer 12

Answer 13

Answer 14

Follow-up question: draw the direction of current in this circuit.

Answer 15

Follow-up question: explain how it is possible to determine that \(V_A\) and \(V_B\) will be exactly the same value, prior to performing any mathematical calculations.

Answer 16

Follow-up question #1: without performing any mathematical calculations, determine the effects on all the component voltage drops and currents if resistor \(R_2\) were to fail open.

Follow-up question #2: without performing any mathematical calculations, determine the effects on all the component voltage drops and currents if resistor \(R_2\) were to fail shorted.

Answer 17

Answer 18

Answer 19

Overloaded wiring gets hot – perhaps enough to start a fire.

A shorted component could cause excessive current in a circuit, but an open fault will result in less (or no) current.

Answer 20

A fuse is for one-time use, while a circuit breaker may be re-set and used repeatedly.

Answer 21

Generally speaking, distribution panel overcurrent protection devices are rated in such a way as to protect the wiring, not the load devices.

Follow-up question: suppose a computer with a 300 watt power supply is plugged into a receptacle, which is serviced by a circuit breaker rated at 15 amps. Where in the circuit would it be best to install an overcurrent protection device for protecting the computer from burning itself up in the event of an internal failure?

Answer 22

So long as the switch is still in the "on" position when these measurements were taken, one of the fuses could still be blown!

Follow-up question: what voltage measurement(s) would conclusively test the condition of both fuses?

Answer 23

Yes, if the power switch is turned "on".

Answer 24

The ground wire connection makes the metal case of the appliance electrically common with earth ground.

Answer 25

Using the neutral conductor as a safety ground is a bad idea, in the event the neutral wire were to ever fail "open" between the receptacle and the system ground point.

Answer 26

Demo Problems

Answer 27

This is a graded problem. No answers given.

Answer 28

Additional Practice Problems

Answer 29

Answer 30

\(V_A =\) 65.28 V

\(V_B =\) -76.74 V

\(V_{AB} =\) 142.02 V (point A being positive relative to point B)

If you are experiencing difficulty in your analysis of this circuit, you might want to refer to this re-drawing:

To make it even easier to visualize, remove the ground symbols and insert a wire connecting the lower wires of each circuit together:

It’s all the same circuit, just different ways of drawing it!

Follow-up question: identify, for a person standing on the ground (with feet electrically common to the ground symbols in the circuits), all the points on the circuits which would be safe to touch without risk of electric shock.

Answer 31

The key to understanding this circuit is that both batteries are equal in voltage and opposed in polarity to one another.

Answer 32

Answer 33

Switch ON:

Switch OFF:

Follow-up question: explain why there will be voltage or no voltage between each of these pairs of points for the two circuit conditions (switch on and switch off).

Answer 34

There are many different sets of resistor values that will achieve this design goal!

Answer 35

Voltage across each resistor = 1.5 V

Current through each resistor = 1.5 mA

Power dissipated by each resistor = 2.25 mW

Voltage ratio = \(1 \over 3\)

Resistance ratio = \(1 \over 3\)

Follow-up question: are the two ratios’ equality a coincidence? Explain your answer.

Answer 36

Disconnect the power supply from the circuit board (only one wire need be disconnected), and then use an ohmmeter to measure continuity across the switch terminals when in the "ON" position and when in the "OFF" position. Incidentally, this is not the only way to check the switch’s continuity, but it is the most direct.

Answer 37

Follow-up question: draw the direction of current in this circuit.

Answer 38

Follow-up question: if each of these batteries outputs a voltage of 1.5 volts, how much voltage does the light bulb experience?

Answer 39

\(I_{R1} = 2.22\) mA ; \(V_{R1} = 3.33\) V

\(I_{R2} = 2.22\) mA ; \(V_{R2} = 22.2\) V

\(I_{R3} = 2.22\) mA ; \(V_{R3} = 10.4\) V

Answer 40

\(V_{TP1-TP3}\) = 15.83 volts \(V_{TP2-TP4}\) = 22.22 volts

Answer 41

First scenario: & Second scenario: \(E_{R1} = 0.225\) volts & \(E_{R1} = 0.45\) volts \(E_{R2} = 7.05\) volts & \(E_{R2} = 14.1\) volts \(E_{R3} = 0.375\) volts & \(E_{R3} = 0.75\) volts \(E_{R4} = 1.35\) volts & \(E_{R4} = 2.7\) volts

Follow-up question: what do you notice about the ratios of the voltages between the two scenarios?

Answer 42

A fuse is a thin piece of metal designed to melt into two pieces in an overcurrent condition.

Answer 43

Answer 44

With each successive step, one more voltage is being added to the previously measured voltage(s), as the meter measures across a larger series chain of resistors. Ultimately,

Answer 45

\(V_A =\) + 65.28 V

\(V_B =\) + 23.26 V

\(V_{AB} =\) + 42.02 V (point A being positive relative to point B)

Challenge question: what would change if the wire connecting the two voltage divider circuits together were removed?

Answer 46

Bear in mind that this is not the only possible circuit solution:

Challenge yourself by designing a different circuit to meet the same criteria!

Answer 47

\(R_3\) = 65.9 k\(\Omega\)

Answer 48

Bear in mind that this is not the only possible circuit solution!

Challenge yourself by designing a different circuit to meet the same criteria!

Answer 49

Bear in mind that this is not the only possible circuit solution:

Challenge yourself by designing a different circuit to meet the same criteria!

Answer 50

This is perhaps the most direct solution (setting each power supply to output 12 volts):

Answer 51

Follow-up question: being that 30 volts is the commonly accepted "danger" threshold voltage for electric shock, determine whether or not this particular circuit poses a shock hazard.

Answer 52

Here is a schematic diagram to help you:

Answer 53

Here is a schematic diagram to help you:

Answer 54

Follow-up question: if we allow ourselves to consider more than one fault occurring at the same time, does the "switch failed shorted" scenario become possible? Explain why or why not.

Answer 55

Note how all the voltage drops are a certain proportion of the total voltage. What do you think would happen to these voltage drops if the source voltage (9 volts from the battery) were doubled?

Answer 56

There are many different sets of resistor values that will achieve this design goal, but here is one pair of resistance values that will suffice:

Answer 57

Kuphaldt, Tony. "Socratic Electronics." Socratic Electronics. Ibiblio.org, n.d. Web. 28 Dec. 2014.

Kuphaldt, Tony. "Socratic Instrumentation." Socratic Instrumentation. Ibiblio.org, n.d. Web. 29 Jan. 2016.

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