Q: A hospital uses a backup battery system with internal resistance. If the battery is rated at 12 V and 0.5 $$\Omega$$ internal resistance, what is the terminal voltage when supplying 10 A to the emergency circuit?

$$V = 12 - (10 \times 0.5) = 7\ \mathrm{V}$$

Question 1

A battery with an emf of 24 V and an internal resistance of 2 $$\Omega is $$connected to a 10 $$\Omega$$ resistor. What is the current in the circuit?

Accepted Answer

$$I = \frac{24}{10 + 2} = 2.0\ \mathrm{A}$$

Question 2

Which of the following correctly expresses the power delivered to a circuit element in terms of current and potential difference?

Accepted Answer

$$P = IV$$

Question 3

If a charge $$q$$ passes through a circuit element with a potential difference $$V_{ab}$$, what is the work done on the charge?

Accepted Answer

$$W = qV_{ab}$$

Question 4

For three resistors $$R_1$$, $$R_2$$, and $$R_3$$ connected in series, what is the equivalent resistance?

Accepted Answer

$$R_{eq} = R_1$ + R_2$ + R_3$

Question 5

For three resistors $$R_1$$, $$R_2$$, and $$R_3$$ connected in parallel, what is the equivalent resistance?

Accepted Answer

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

Question 6

A circuit contains a battery of emf $$\mathcal{E}$$ and three resistors $$R_1 = 4$$\ \Omega$$, R_2$ = 2\ \Omega$$, and $$R_3 = 3$$\ \Omega$$ in series. What is the total current if $$\mathcal{E} = 12\ \mathrm{V}$$?

Accepted Answer

$$I = \frac{12}{4 + 2 + 3} = 1.09\ \mathrm{A}$$

Question 7

In a parallel circuit, which quantity is the same for all resistors?

Accepted Answer

The voltage across each resistor

Question 8

A resistor network consists of $$R_1 = 3$$\ \Omega$$ and R_2$ = 6\ \Omega. $$What is the equivalent resistance if they are connected in parallel?

Accepted Answer

$$R_{eq} = \frac{1}{\frac{1}{3} + \frac{1}{6}} = 2\ \Omega$$

Question 9

What is the unit of electrical power?

Accepted Answer

Watt

Question 10

A switch in a parallel resistor network is closed, adding another resistor in parallel. What happens to the total current supplied by the battery?

Accepted Answer

It increases

Question 11

If a resistor $$R$$ dissipates power $$P$$ when a voltage $$V is $$applied, which formula correctly relates these quantities?

Accepted Answer

$$P = \frac{V^2$}{R}$$

Question 12

A battery with emf $$\mathcal{E}$$ and internal resistance $$r is $$connected to a load resistor $$R. $$What is the terminal voltage across the load resistor?

Accepted Answer

$$V = \mathcal{E} - Ir$$

Question 13

Which of the following is true for resistors in series?

Accepted Answer

The current through each resistor is the same

Question 14

A circuit element has a potential difference $$V_{ab}$$ and a current $$I$$ passing through it for a time interval $$\Delta t. $$What is the total work done?

Accepted Answer

$$\Delta W = V$$_{ab}$$I\Delta t$$

Question 15

Which equation gives the total charge passing through a circuit element in a time interval $$\Delta t$$?

Accepted Answer

$$\Delta Q = I\Delta t$$

Question 16

A battery provides power to a circuit, but some energy is lost due to internal resistance. Which real-world effect does this describe?

Accepted Answer

The battery heats up during use

Question 17

Which formula correctly expresses the potential energy stored in a capacitor?

Accepted Answer

$$U = \frac{1}{2}CV^2$

Question 18

A hospital uses a backup battery system with internal resistance. If the battery is rated at 12 V and 0.5 $$\Omega$$ internal resistance, what is the terminal voltage when supplying 10 A to the emergency circuit?

Accepted Answer

$$V = 12 - (10 	imes 0.5) = 7\ \mathrm{V}$$

Question 19

A resistor network consists of $$R_1 = 2$$\ \Omega$$, R_2$ = 4\ \Omega$$, and $$R_3 = 8$$\ \Omega$$ in parallel. What is the equivalent resistance?

Accepted Answer

$$R_{eq} = \frac{1}{\frac{1}{2} + \frac{1}{4} + \frac{1}{8}} = 1.14\ \Omega$$

Chapter 19: Current, Resistance, and DC Circuits – Study Notes

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