Q: Immediately after the switch is closed in the RC circuit, what is the initial current $$I_0$$ through the equivalent resistor $$R_{eq}$$? (Given $$q = 100 nC$$, $$C = 1.0$$ μF, $$R_{eq} = 58\ \Omega)$$

$$I_0$$ = \frac{q}{C R_{eq}} = \frac{100 \times $$10^{-9}$$\ \mathrm{C}}{1.0 \times $$10^{-6}$$\ \mathrm{F} \times 58\ \Omega} = 1.72\ \mathrm{mA}$$

Q: At what time $$t$$ after the switch is closed will the current in the RC circuit have decreased to $$I = 0.37 I_0$?

$$t = R_{eq} C = 58\ \Omega \times 1.0 \times 10$$^{-6}$$\ \mathrm{F} = 58\ \mu\mathrm{s}$$

Q: If a $$40\ \Omega$$ resistor has a current of $$0.5\ \mathrm{A}$$ flowing through it, how much power is dissipated?

$$P = (0.5)^2$ \times 40 = 10\ \mathrm{W}$$

Q: A sensitive instrument measures the heat generated by two resistors in series: $$40\ \Omega$$ and $$50\ \Omega. If $$the same current flows through both, which equation correctly compares the heat generated over time $$t$$?

$$Q_{50} \u003e Q_{40}$$, \text{ since } Q = $$I^2 R t$

Question 1

A circuit contains a 1.0 μF capacitor charged to $$+q = 100 nC $$and three resistors: $$R_1 = 50$$\ \Omega$$, R_2$ = 10\ \Omega$$, and $$R_3 = 40$$\ \Omega$$. If R_2$ and R_3$ are in parallel and their combination is in series with R_1$, what is the equivalent resistance R$$_{eq}$$ of the circuit?

Accepted Answer

$$R_{eq} = 50\ \Omega + \left(\frac{1}{\frac{1}{10\ \Omega} + \frac{1}{40\ \Omega}}\right) = 58\ \Omega$$

Question 2

Immediately after the switch is closed in the RC circuit, what is the initial current $$I_0$$ through the equivalent resistor $$R_{eq}$$? (Given $$q = 100 nC$$, $$C = 1.0$$ μF, $$R_{eq} = 58\ \Omega)$$

Accepted Answer

$$I_0$$ = \frac{q}{C R_{eq}} = \frac{100 	imes $$10^{-9}$$\ \mathrm{C}}{1.0 	imes $$10^{-6}$$\ \mathrm{F} 	imes 58\ \Omega} = 1.72\ \mathrm{mA}$$

Question 3

At what time $$t$$ after the switch is closed will the current in the RC circuit have decreased to $$I = 0.37 I_0$?

Accepted Answer

$$t = R_{eq} C = 58\ \Omega 	imes 1.0 	imes 10$$^{-6}$$\ \mathrm{F} = 58\ \mu\mathrm{s}$$

Question 4

In the diagram with two parallel wires, Wire 1 carries current $$I to $$the left and Wire 2 carries current $$2I to $$the right. What is the direction of the magnetic field at point C (above both wires)?

Accepted Answer

The magnetic field at C points out of the page toward the observer.

Question 5

What is the direction of the magnetic field at point D (between the two wires)?

Accepted Answer

The magnetic field at D points into the page away from the observer.

Question 6

What is the direction of the magnetic field at point E (below both wires)?

Accepted Answer

The magnetic field at E points out of the page toward the observer.

Question 7

A $$40\ \Omega$$ resistor and a $$50\ \Omega$$ resistor are in series in a circuit. If the same current flows through both, which resistor will generate more heat over the same period of time?

Accepted Answer

The $$50\ \Omega$$ resistor will generate more heat.

Question 8

Given a resistor with resistance $$R$$ and current $$I$$ flowing through it, what is the power dissipated by the resistor?

Accepted Answer

$$P = I^2$ R$$

Question 9

If a $$40\ \Omega$$ resistor has a current of $$0.5\ \mathrm{A}$$ flowing through it, how much power is dissipated?

Accepted Answer

$$P = (0.5)^2$ 	imes 40 = 10\ \mathrm{W}$$

Question 10

In a parallel plate capacitor circuit, what is the direction of electron flow immediately after the switch is closed?

Accepted Answer

Electrons flow from the negative plate of the capacitor through the resistor toward the positive plate.

Question 11

Which equation describes the time-dependent current $$I(t) in an RC $$circuit after the switch is closed?

Accepted Answer

$$I(t) = I_0$ e$$^{-t/(RC)}$$

Question 12

A sensitive instrument measures the heat generated by two resistors in series: $$40\ \Omega$$ and $$50\ \Omega. If $$the same current flows through both, which equation correctly compares the heat generated over time $$t$$?

Accepted Answer

$$Q_{50} \u003e Q_{40}$$, 	ext{ since } Q = $$I^2 R t$

Question 13

If the voltage across a $$40\ \Omega$$ resistor is $$20\ \mathrm{V}$$, what is the current through the resistor?

Accepted Answer

$$I = \frac{V}{R} = \frac{20}{40} = 0.5\ \mathrm{A}$$

Question 14

Which of the following best describes the effect of increasing the resistance in an RC circuit on the time constant $$	au$$?

Accepted Answer

Increasing resistance increases the time constant $$	au = RC.$$

Physics 153-1 Exam 2 Study Guidance: Circuits, Magnetism, and Capacitors

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