Q: A battery is modeled as a source of emf $$e in $$series with an internal resistance $$r. If a $$battery with $$e = 12.0 V $$and $$r = 0.5 \ \Omega is $$connected to a resistor $$R = 65.0 \ \Omega$$, what is the terminal voltage of the battery when a current flows?

$$V_{ab} = e - Ir = 12.0 \text{ V} - (0.183 \text{ A})(0.5 \ \Omega) = 11.9 \text{ V}$$

Q: A circuit contains two batteries: one with $$e_1 = 80$ V and r_1$ = 1 \ \Omega$$, and another with $$e_2 = 45$ V and r_2$ = 1 \ \Omega. If $$the batteries are connected in series but with opposite polarity, what is the net voltage applied to the circuit?

$$80 \text{ V} - 45 \text{ V} = 35 \text{ V}$$

Q: A $$0.30 mF $$capacitor is charged through a $$20 k$\Omega$$ resistor by a $$12 V $$battery. What is the time constant $$\tau$$ for this RC circuit?

$$\tau = RC = (2.0 \times 10^4$ \ \Omega)(3.0 \times 10$$^{-7}$$ \text{ F}) = 6.0 \times 10$$^{-3}$$ \text{ s}$$

Question 1

A battery is modeled as a source of emf $$e in $$series with an internal resistance $$r. If a $$battery with $$e = 12.0 V $$and $$r = 0.5 \ \Omega is $$connected to a resistor $$R = 65.0 \ \Omega$$, what is the terminal voltage of the battery when a current flows?

Accepted Answer

$$V_{ab} = e - Ir = 12.0 	ext{ V} - (0.183 	ext{ A})(0.5 \ \Omega) = 11.9 	ext{ V}$$

Question 2

Which equation correctly describes the equivalent resistance for three resistors $$R_1$$, $$R_2$$, and $$R_3$$ connected in parallel?

Accepted Answer

$$\frac{1}{R_{eq}} = \frac{1}{R_1$} + \frac{1}{R_2$} + \frac{1}{R_3$}$$

Question 3

A car's headlights are wired in parallel. What is the main advantage of this configuration compared to wiring them in series?

Accepted Answer

If one bulb burns out, the other can stay lit.

Question 4

In a circuit with a $$9.0 V $$battery and internal resistance $$r = 0.5 \ \Omega$$, two resistors $$6.0 \ \Omega$$ and $$2.7 \ \Omega$$ are in series, and two resistors $$8.0 \ \Omega$$ and $$4.0 \ \Omega$$ are in parallel. What is the total equivalent resistance of the circuit?

Accepted Answer

$$R_{eq} = 10.3 \ \Omega$$

Question 5

Kirchhoff’s junction rule is based on which physical principle?

Accepted Answer

Conservation of charge

Question 6

A circuit contains two batteries: one with $$e_1 = 80$ V and r_1$ = 1 \ \Omega$$, and another with $$e_2 = 45$ V and r_2$ = 1 \ \Omega. If $$the batteries are connected in series but with opposite polarity, what is the net voltage applied to the circuit?

Accepted Answer

$$80 	ext{ V} - 45 	ext{ V} = 35 	ext{ V}$$

Question 7

Which formula gives the equivalent capacitance for three capacitors $$C_1$$, $$C_2$$, and $$C_3$$ connected in series?

Accepted Answer

$$\frac{1}{C_{eq}} = \frac{1}{C_1$} + \frac{1}{C_2$} + \frac{1}{C_3$}$$

Question 8

A $$0.30 mF $$capacitor is charged through a $$20 k$\Omega$$ resistor by a $$12 V $$battery. What is the time constant $$	au$$ for this RC circuit?

Accepted Answer

$$	au = RC = (2.0 	imes 10^4$ \ \Omega)(3.0 	imes 10$$^{-7}$$ 	ext{ F}) = 6.0 	imes 10$$^{-3}$$ 	ext{ s}$$

Question 9

Which of the following best describes the function of a heart pacemaker as seen in the X-ray image?

Accepted Answer

It uses an RC circuit to produce regular voltage pulses that stimulate the heart.

Question 10

A digital voltmeter is used to measure the voltage across a resistor. Which property of the voltmeter ensures it does not significantly affect the circuit being measured?

Accepted Answer

It has a very high internal resistance.

Question 11

A person is using a hair dryer near a sink, as shown in the image. What is the main electrical hazard in this scenario?

Accepted Answer

The risk of electric shock due to water reducing skin resistance.

Question 12

Which plug configuration provides the safest connection for appliances with metal cases?

Accepted Answer

A three-prong plug, where the third prong grounds the case.

Question 13

A car is being jump-started using jumper cables. If the cables are connected with the positive terminal of one battery to the negative terminal of the other, what is the likely outcome?

Accepted Answer

A very large current will flow, possibly causing battery damage or explosion.

Question 14

Which equation describes the voltage across a charging capacitor in an RC circuit as a function of time?

Accepted Answer

$$V_C(t) = e \left(1 - e$$^{-t/RC}$$\right)$$

Question 15

Which of the following is a correct safety practice when working with electrical circuits?

Accepted Answer

Keep one hand in your pocket when touching electrical equipment.

Question 16

A resistor and a capacitor are used in series to control the timing in a heart pacemaker. To double the heart rate, what should be done to the resistance?

Accepted Answer

Decrease the resistance so the capacitor discharges faster.

Question 17

Which equation describes the exponential decay of voltage across a discharging capacitor in an RC circuit?

Accepted Answer

$$V_C(t) = V_0$ e$$^{-t/RC}$$

Question 18

Which of the following best explains why birds can sit safely on power lines?

Accepted Answer

Both feet are at the same electric potential, so no current flows through the bird.

DC Circuits: Series and Parallel Circuits, Kirchhoff’s Rules, Capacitors, RC Circuits, and Measurement Instruments

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