Q: A 10.0 $$\muF $$capacitor is charged through a 2.0 k$$\Omega$$ resistor. How long does it take for the charge to reach half its final value?

$$t = RC \ln 2 = (2000)(10 \times 10$$^{-6}$$) \ln 2 \approx 0.014\ \mathrm{s}$$

Question 1

A 6.00 $$\Omega$$ and an 8.00 $$\Omega$$ resistor are connected in parallel. What is their equivalent resistance?

Accepted Answer

$$R_{eq} = 3.43\ \Omega$$

Question 2

In the circuit shown, a current of 4.00 A flows through the 6.00 $$\Omega$$ resistor. What is the voltage drop across this resistor?

Accepted Answer

$$V = 24.0\ \mathrm{V}$$

Question 3

Which of the following best describes Kirchhoff’s junction rule?

Accepted Answer

The sum of the currents entering a junction equals the sum of the currents leaving the junction.

Question 4

A 20.0 $$\Omega$$ resistor is in series with a parallel combination of 6.00 $$\Omega$$ and 8.00 $$\Omega$$ resistors. What is the total equivalent resistance?

Accepted Answer

$$R_{eq} = 23.43\ \Omega$$

Question 5

In a charging RC circuit, what is the expression for the charge $$q(t) on $$the capacitor as a function of time?

Accepted Answer

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

Question 6

A capacitor is being charged in an RC circuit. What happens to the current through the resistor as time increases?

Accepted Answer

It decreases exponentially with time.

Question 7

Which of the following is the correct time constant $$	au$$ for an RC circuit?

Accepted Answer

$$	au = RC$$

Question 8

A 10.0 $$\muF $$capacitor is charged through a 2.0 k$$\Omega$$ resistor. How long does it take for the charge to reach half its final value?

Accepted Answer

$$t = RC \ln 2 = (2000)(10 	imes 10$$^{-6}$$) \ln 2 \approx 0.014\ \mathrm{s}$$

Question 9

In a discharging RC circuit, what is the expression for the current $$i(t) as a $$function of time?

Accepted Answer

$$i(t) = \frac{Q_0$}{RC} e$$^{-t/RC}$$

Question 10

A 13 V battery is connected to a network of five resistors as shown in a bridge circuit. If the total current supplied by the battery is 11 A, what is the equivalent resistance of the network?

Accepted Answer

$$R_{eq} = 1.2\ \Omega$$

Question 11

Which of the following statements about the loop rule is correct?

Accepted Answer

The sum of the potential differences around any closed loop is zero.

Question 12

If the area of a resistor is doubled while keeping its length constant, what happens to its resistance?

Accepted Answer

It is halved.

Question 13

In a parallel circuit, which of the following is true about the voltage across each resistor?

Accepted Answer

It is the same for all resistors.

Question 14

A 4.00 $$\Omega$$ and a 2.00 $$\Omega$$ resistor are connected in series. What is the total resistance?

Accepted Answer

$$R_{eq} = 6.00\ \Omega$$

Question 15

Which of the following best describes the water-pipe analogy for Kirchhoff’s junction rule?

Accepted Answer

The flow rate of water leaving the pipe equals the flow rate entering it.

Question 16

A capacitor is initially charged to $$Q_0$$ and then allowed to discharge through a resistor $$R. $$What is the charge on the capacitor after a time $$t$$?

Accepted Answer

$$q(t) = Q_0$ e$$^{-t/RC}$$

Question 17

In a real-world application, why is the time constant $$	au = RC$$ important in the design of defibrillators?

Accepted Answer

It determines how quickly the capacitor can discharge to deliver a pulse.

Question 18

If a battery with emf $$\mathcal{E}$$ and negligible internal resistance is connected to a series combination of resistors $$R_1$$ and $$R_2$$, what is the current in the circuit?

Accepted Answer

$$I = \frac{\mathcal{E}}{R_1$ + R_2$}$$

Direct-Current Circuits: Series & Parallel Resistors, Kirchhoff’s Rules, and R-C Circuits

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