Q: A circuit consists of a $$12\ \text{V}$$ battery connected to a $$4\ \Omega$$ resistor and a $$2\ \Omega$$ resistor in series. What is the current flowing through the circuit?

$$12\ \text{V} / (4\ \Omega + 2\ \Omega) = 2\ \text{A}$$

Q: If a $$10\ \mu\text{F}$$ capacitor is charged to $$100\ \text{V}$$, how much energy is stored in the capacitor?

$$U = \frac{1}{2}CV^2$ = \frac{1}{2} \times 10 \times 10$$^{-6}$$ \times (100)^2$ = 0.05\ \text{J}$$

Q: A $$100\ \Omega$$ resistor is connected to a $$10\ \text{V}$$ battery. How much power is dissipated in the resistor?

$$P = \frac{V^2$}{R} = \frac{10^2$}{100} = 1\ \text{W}$$

Q: A $$5\ \Omega$$ and a $$10\ \Omega$$ resistor are connected in parallel across a $$20\ \text{V}$$ battery. What is the total current supplied by the battery?

$$I = \frac{20}{5} + \frac{20}{10} = 4 + 2 = 6\ \text{A}$$

Question 1

A parallel-plate capacitor is connected to a battery and fully charged. If the battery is then disconnected and a dielectric is inserted between the plates, what happens to the energy stored in the capacitor?

Accepted Answer

The energy stored decreases because the voltage across the plates decreases.

Question 2

Which of the following correctly expresses the energy stored in a capacitor in terms of its capacitance $$C$$ and the potential difference $$V$$ across its plates?

Accepted Answer

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

Question 3

A copper wire and a carbon rod have the same length and cross-sectional area. Which one has the lower resistance and why?

Accepted Answer

The copper wire, because copper has a lower resistivity than carbon.

Question 4

If three capacitors with capacitances $$C_1$$, $$C_2$$, and $$C_3$$ are connected in parallel, what is the equivalent capacitance $$C_{eq}$$?

Accepted Answer

$$C_{eq} = C_1$ + C_2$ + C_3$

Question 5

A resistor of resistance $$R is $$connected to a battery of voltage $$V. $$What is the power dissipated as heat in the resistor?

Accepted Answer

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

Question 6

Which of the following statements about electric current is correct?

Accepted Answer

Current is defined as the net flow of charge per unit time, and its direction is from high potential to low potential by convention.

Question 7

A wire of length $$L$$ and cross-sectional area $$A is $$made of a material with resistivity $$\rho. $$What is the resistance $$R of $$the wire?

Accepted Answer

$$R = \frac{\rho L}{A}$$

Question 8

Two resistors, $$R_1 = 2$$\ \Omega$$ and R_2$ = 6\ \Omega$$, are connected in parallel. What is the equivalent resistance $$R_{eq}$$?

Accepted Answer

$$R_{eq} = 1.5\ \Omega$$

Question 9

A circuit consists of a $$12\ 	ext{V}$$ battery connected to a $$4\ \Omega$$ resistor and a $$2\ \Omega$$ resistor in series. What is the current flowing through the circuit?

Accepted Answer

$$12\ 	ext{V} / (4\ \Omega + 2\ \Omega) = 2\ 	ext{A}$$

Question 10

If a $$10\ \mu	ext{F}$$ capacitor is charged to $$100\ 	ext{V}$$, how much energy is stored in the capacitor?

Accepted Answer

$$U = \frac{1}{2}CV^2$ = \frac{1}{2} 	imes 10 	imes 10$$^{-6}$$ 	imes (100)^2$ = 0.05\ 	ext{J}$$

Question 11

A $$9\ 	ext{V}$$ battery is connected to a circuit with two resistors, $$R_1 = 3$$\ \Omega$$ and R_2$ = 6\ \Omega$$, in series. What is the voltage drop across $$R_2$$?

Accepted Answer

$$6\ 	ext{V}$$

Question 12

Which of the following best describes the effect of increasing the cross-sectional area of a wire on its resistance, assuming all other factors remain constant?

Accepted Answer

The resistance decreases because resistance is inversely proportional to area.

Question 13

A $$100\ \Omega$$ resistor is connected to a $$10\ 	ext{V}$$ battery. How much power is dissipated in the resistor?

Accepted Answer

$$P = \frac{V^2$}{R} = \frac{10^2$}{100} = 1\ 	ext{W}$$

Question 14

If a dielectric material with dielectric constant $$K is $$inserted into a capacitor while the voltage is kept constant, what happens to the capacitance and the energy stored?

Accepted Answer

Capacitance increases and energy stored increases.

Question 15

Which of the following is true for resistors connected in series?

Accepted Answer

The total resistance is the sum of the individual resistances.

Question 16

A $$5\ \Omega$$ and a $$10\ \Omega$$ resistor are connected in parallel across a $$20\ 	ext{V}$$ battery. What is the total current supplied by the battery?

Accepted Answer

$$I = \frac{20}{5} + \frac{20}{10} = 4 + 2 = 6\ 	ext{A}$$

Question 17

Which of the following best explains why a resistor gets hot when current flows through it?

Accepted Answer

The resistor converts electrical energy into thermal energy due to collisions inside the wire.

Question 18

A $$12\ 	ext{V}$$ battery is connected to a circuit with a $$3\ \Omega$$ resistor and a $$6\ \Omega$$ resistor in parallel. What is the equivalent resistance of the circuit?

Accepted Answer

$$R_{eq} = 2\ \Omega$$

Question 19

Which of the following is the correct expression for Ohm’s Law?

Accepted Answer

$$V = IR$$

Resistance, Ohm’s Law, and Electric Circuits: Study Notes

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