Q: A 120 V potential difference is applied across a Nichrome wire with resistance $$R = 72\ \Omega. $$What is the rate of energy dissipation in the wire?

$$P = \frac{V^2$}{R} = \frac{120^2$}{72} = 200\ \text{W}$$

Q: If the wire in the previous question is cut in half and the same 120 V potential difference is applied across each half, what is the new rate of energy dissipation in one half?

$$P = \frac{V^2$}{R} = \frac{120^2$}{36} = 400\ \text{W}$$

Q: In a series circuit with resistors $$R_1 = 1$$\ \Omega$$, R_2$ = 2\ \Omega$$, and $$R_3 = 3$$\ \Omega$$ connected to a 12 V battery, what is the total resistance?

$$R_{\text{total}} = R_1$ + R_2$ + R_3$ = 6\ \Omega$$

Q: What is the current through each resistor in the series circuit described above?

$$I = \frac{V}{R_{\text{total}}} = \frac{12}{6} = 2\ \text{A}$$

Q: In a parallel circuit with resistors $$R_1 = 5$$\ \Omega$$, R_2$ = 7\ \Omega$$, and $$R_3 = 9$$\ \Omega$$ connected to an 8 V battery, what is the equivalent resistance?

$$\frac{1}{R_{\text{eq}}} = \frac{1}{5} + \frac{1}{7} + \frac{1}{9} \Rightarrow R_{\text{eq}} \approx 2.2\ \Omega$$

Q: What is the current through the 9 $$\Omega$$ resistor in the parallel circuit above?

$$I = \frac{V}{R} = \frac{8}{9} \approx 0.89\ \text{A}$$

Q: A circuit contains a battery with emf $$\epsilon$$ and internal resistance $$R_{\text{int}}. $$What is the terminal voltage $$V_{ab}$$ when a current $$i$$ flows?

$$V_{ab} = \epsilon - iR_{\text{int}}$$

Question 1

A 120 V potential difference is applied across a Nichrome wire with resistance $$R = 72\ \Omega. $$What is the rate of energy dissipation in the wire?

Accepted Answer

$$P = \frac{V^2$}{R} = \frac{120^2$}{72} = 200\ 	ext{W}$$

Question 2

If the wire in the previous question is cut in half and the same 120 V potential difference is applied across each half, what is the new rate of energy dissipation in one half?

Accepted Answer

$$P = \frac{V^2$}{R} = \frac{120^2$}{36} = 400\ 	ext{W}$$

Question 3

In a series circuit with resistors $$R_1 = 1$$\ \Omega$$, R_2$ = 2\ \Omega$$, and $$R_3 = 3$$\ \Omega$$ connected to a 12 V battery, what is the total resistance?

Accepted Answer

$$R_{	ext{total}} = R_1$ + R_2$ + R_3$ = 6\ \Omega$$

Question 4

What is the current through each resistor in the series circuit described above?

Accepted Answer

$$I = \frac{V}{R_{	ext{total}}} = \frac{12}{6} = 2\ 	ext{A}$$

Question 5

In a parallel circuit with resistors $$R_1 = 5$$\ \Omega$$, R_2$ = 7\ \Omega$$, and $$R_3 = 9$$\ \Omega$$ connected to an 8 V battery, what is the equivalent resistance?

Accepted Answer

$$\frac{1}{R_{	ext{eq}}} = \frac{1}{5} + \frac{1}{7} + \frac{1}{9} \Rightarrow R_{	ext{eq}} \approx 2.2\ \Omega$$

Question 6

What is the current through the 9 $$\Omega$$ resistor in the parallel circuit above?

Accepted Answer

$$I = \frac{V}{R} = \frac{8}{9} \approx 0.89\ 	ext{A}$$

Question 7

Which statement about current in a parallel circuit is correct?

Accepted Answer

The total current is the sum of the currents through each branch: $$I_{	ext{total}} = I_1$ + I_2$ + I_3$

Question 8

A circuit contains a battery with emf $$\epsilon$$ and internal resistance $$R_{	ext{int}}. $$What is the terminal voltage $$V_{ab}$$ when a current $$i$$ flows?

Accepted Answer

$$V_{ab} = \epsilon - iR_{	ext{int}}$$

Question 9

Kirchhoff’s junction rule states:

Accepted Answer

The sum of the currents into any junction equals zero: $$\sum I = 0$$

Question 10

Kirchhoff’s loop rule states:

Accepted Answer

The sum of the potential differences around any closed loop equals zero: $$\sum V = 0$$

Question 11

In a circuit with a resistor and a capacitor, the charge on the capacitor during discharge is given by:

Accepted Answer

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

Question 12

During the charging of a capacitor in an RC circuit, the current as a function of time is:

Accepted Answer

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

Question 13

A fuse in a household circuit is designed to:

Accepted Answer

Melt and break the circuit when its rated current is exceeded.

Question 14

Which device can be reset after it trips due to excessive current?

Accepted Answer

Circuit breaker

Question 15

In a household wiring system, the neutral line is connected to:

Accepted Answer

Ground

Question 16

If a circuit contains both series and parallel resistors, how do you find the total resistance?

Accepted Answer

Reduce the circuit stepwise using series and parallel rules to find equivalent resistances.

Question 17

In a series circuit, what happens to the voltage across each resistor?

Accepted Answer

The voltage drop across each resistor adds up to the total voltage supplied.

Question 18

In a parallel circuit, what happens to the voltage across each resistor?

Accepted Answer

Each resistor has the same voltage across it, equal to the supply voltage.

Electric Circuits: Power, Series and Parallel Circuits, Kirchhoff’s Rules, and RC Circuits

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