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## End of chapter exercises

Write definitions for each of the following:

1. resistor

2. coulomb

3. voltmeter

a) A resistor is a physical component of a circuit that has resistance. Resistance is defined as the ratio of the voltage and the current through a physical component, as defined by Ohm's law.

b) A coulomb is a unit of charge.

c) A voltmeter is a device that measures the potential difference (in Volts) across a physical component, when connected in parallel with that component.

Draw a circuit diagram which consists of the following components:

1. 2 batteries in parallel

2. an open switch

3. 2 resistors in parallel

4. an ammeter measuring total current

5. a voltmeter measuring potential difference across one of the parallel resistors

Complete the table below:

 Quantity Symbol Unit of measurement Symbol of unit e.g. Distance e.g. D e.g. kilometre e.g. km Resistance Current Potential difference

[SC 2003/11] The emf of a battery can best be explained as the $...$

1. rate of energy delivered per unit current

2. rate at which charge is delivered

3. rate at which energy is delivered

4. charge per unit of energy delivered by the battery

d.

rate of energy delivered per unit current

[IEB 2002/11 HG1] Which of the following is the correct definition of the emf of a battery?

1. It is the product of current and the external resistance of the circuit.

2. It is a measure of the cell's ability to conduct an electric current.

3. It is equal to the “lost volts” in the internal resistance of the circuit.

4. It is the power supplied by the battery per unit current passing through the battery.

d.

It is the power supplied by the battery per unit current passing through the battery.

[IEB 2005/11 HG] Three identical light bulbs A, B and C are connected in an electric circuit as shown in the diagram below.

1. How bright is bulb A compared to B and C?

2. How bright are the bulbs after switch S has been opened?

3. How do the currents in bulbs A and B change when switch S is opened?

 Current in A Current in B (a) decreases increases (b) decreases decreases (c) increases increases (d) increases decreases

a) Bulb A will be brighter than B and C as there is more current flowing through it.

b) Bulb A and B will be equally bright, but bulb C will not be lit up. (When the switch opens, no current flows through bulb C and bulbs A and B are now in series.)

c) b

[IEB 2004/11 HG1] When a current Iis maintained in a conductor for a time of t, how many electrons with charge e pass any cross-section of the conductor per second?

1. It

2. It/e

3. Ite

4. e/It

d.

It

If you have a circuit consisting of 4 resistors of equal resistance in series and the total voltage across all of them is 17 V, what is the voltage across each of them?

Resistance of 1 resistor is ${V}_{R}$. In series the resistors are voltage dividers and identical, so the voltage across each is the same. The voltage across the battery will be equal to the sum of voltage in a series circuit.

${V}_{\text{battery}}={V}_{R}+{V}_{R}+{V}_{R}+{V}_{R}$

$17\text{V}=4{V}_{R}$

${V}_{R}=\frac{17}{4}=4,25\text{V}$

If you have a circuit consisting of 4 resistors of equal resistance in parallel and the total voltage across all of them is 17 V, what is the voltage across each of them?

The voltage across the parallel set up is the same as the voltage across each resistor.

So the voltage across each resistor is 17 V

In a circuit consisting of a battery and 3 resistors in series, what is the voltage across the first resistor if the voltage across the battery is 12 V and the voltages across the other two resistors is 3 V and 2 V respectively?

${V}_{s}={V}_{1}+{V}_{2}+l\stackrel{.}{s}$

$12\text{V}=3\text{V}+2\text{V}+{V}_{unknown}$

${V}_{unknown}=7\text{V}$

There are 3 resistors in parallel with resistances of 3 Ω, 4 Ω and 11 Ω. What is the total resistance of the parallel combination?

${R}_{1}=3\Omega ,\text{}{R}_{2}=4\Omega ,\text{}{R}_{3}=11\Omega$

${\frac{1}{R}}_{P}={\frac{1}{R}}_{1}+{\frac{1}{R}}_{2}+{\frac{1}{R}}_{3}$

${R}_{P}=\frac{{R}_{1}{R}_{2}{R}_{3}}{{R}_{1}{R}_{2}+{R}_{2}{R}_{3}+{R}_{1}{R}_{3}}$

${R}_{P}=\frac{\left(3\right)\left(4\right)\left(11\right)}{12+44+33}$

${R}_{P}=\frac{132}{89}$

${R}_{P}=1,4\Omega$

The same three resistors as above are now arranged in series, 3 Ω, 4 Ω and 11 Ω. What is the total resistance of the series combination?

${R}_{S}={R}_{1}+{R}_{2}+{R}_{3}$

${R}_{S}=3+4+11$

${R}_{S}=18\Omega$

The total resistance of two resistors in parallel is 3 Ω, the one resistor has a resistance of 5 Ω, what is the resistance of the other resistor?

${R}_{P}=3\Omega \text{}{R}_{1}=5\Omega \text{and}{R}_{2}=?$

${R}_{P}=\frac{{R}_{1}{R}_{2}}{{R}_{1}+{R}_{2}}$

${R}_{P}\left({R}_{1}+{R}_{2}\right)={R}_{1}{R}_{2}$

${R}_{P}{R}_{1}+{R}_{P}{R}_{2}-{R}_{1}{R}_{2}=0$

${R}_{2}\left({R}_{P}-{R}_{1}\right)=-{R}_{P}{R}_{1}$

${R}_{2}=\frac{-{R}_{P}{R}_{1}}{{R}_{P}-{R}_{1}}$

${R}_{2}=\frac{-\left(3\right)\left(5\right)}{3-5}$

${R}_{2}=\frac{-15}{-2}$

${R}_{2}=7,5\Omega$

In a series circuit there are 3 resistors with voltages of 2 V, 5 V and 8 V, what is the voltage across the battery in the circuit?

${V}_{\text{battery}}={V}_{1}+{V}_{2}+{V}_{3}$

${V}_{\text{battery}}=2+5+8$

${V}_{\text{battery}}=15\text{V}$

In a parallel circuit there are 3 resistors with voltages of 2 V, 2 V and 2 V, what is the voltage across the battery in the circuit?

${V}_{\text{battery}}=2V$