Question 1

A wire with a uniform diameter of 2.00 mm and a conduction electron density of $$8.00 	imes 10$$^{27}$$ electrons per m^3$ carries a current of 2.10 A. What is the drift speed of the electrons in the wire? (in m/s)

Use the formula:

I = n e A v_d$$ $$

where I$ is current, n$ is electron density, e$ is elementary charge (1.60$$ 	imes $$10^{-19} C$$), $$A is $$cross-sectional area, and $$v_d is $$drift speed.

Accepted Answer

$$4.46 	imes 10$$^{-4}$$

Question 2

A tungsten filament in a lightbulb is 2.83 cm long and has a resistance of 0.775 $$\Omega. $$The resistivity of tungsten is $$5.60 	imes 10$$^{-8}$$ $$\Omega \cdot m$$. What is the diameter of the filament? (in mm)

Use the formula:

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

Accepted Answer

$$2.17 	imes 10$$^{-2}$$

Question 3

Refer to the junction shown in the first image. Which equation correctly expresses the sum of the currents at the junction according to Kirchhoff's junction rule?

Accepted Answer

$$-i_1$ + i_2$ + i_3$ + i_4$ = 0$$

Question 4

Three resistors ($$19.6 \Omega$$, $$21.1 \Omega$$, $$12.5 \Omega) $$are connected in parallel across 89 V. What is the total resistance for this circuit? (in $$\Omega)

$$Use:

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

Accepted Answer

$$11.7$$

Question 5

A battery with an emf of 12.00 V has an internal resistance $$r. $$When connected to a resistor $$R$$, the terminal voltage is 11.70 V and the current is 0.13 A. What is the value of the external resistor $$R$$? (in $$\Omega)

$$Use:

$$ V_{terminal} = IR $$

Accepted Answer

Question 6

For the same battery and circuit as above, what is the internal resistance $$r of $$the battery? (in $$\Omega)

$$Use:

$$ 	ext{emf} = V_{terminal} + Ir $$

Accepted Answer

$$2.31$$

Question 7

Refer to the second image. If the switch is open, what is the voltage across the switch?

Accepted Answer

$$1.5$$

Question 8

Refer to the third image. Four identical lightbulbs (A–D) are arranged as shown. Rank the order of the lightbulbs based on brightness from brightest to dimmest.

Accepted Answer

A \u003e C = D \u003e B

Question 9

An uncharged capacitor and a resistor are connected in series to a source of EMF. If $$\varepsilon = 8.43 V$$, $$C = 18.6 \muF$$, and $$R = 140 \Omega$$, what is the time constant $$	au of $$the circuit? (in ms)

$$ 	au = RC $$

Accepted Answer

$$2.60$$

Question 10

For the same RC circuit above, what is the current through the resistor after a long time has passed? (in mA)

Accepted Answer

$$0.0$$

Question 11

Two resistors $$R_1 = 16$$ \Omega$$ and R_2$ = 8 \Omega$$ are connected in series to a battery supplying $$\Delta V = 6 V. $$How much power is dissipated by resistor $$R_2$$? (in W)

Use:

$$ P = I^2$ R_2$ $$ where $$I = \frac{\Delta V}{R_1$ + R_2$} $$

Accepted Answer

$$7.80 	imes 10$$^{-2}$$

Question 12

A copper wire is used in a hospital MRI machine. If the wire has a diameter of 3.00 mm and carries a current of 5.00 A, what is the drift speed of electrons? (Assume electron density $$n = 8.50 	imes 10$$^{28}$$ m$$^{-3}$$.)

I = n e A v_d$$ $$

Accepted Answer

$$3.13 	imes 10$$^{-4}$$

Question 13

A resistor is connected to a 24 V battery and dissipates 48 W of power. What is the resistance of the resistor?

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

Accepted Answer

$$12 \Omega$$

Question 14

A circuit contains a battery with emf $$\varepsilon = 9 V$$, internal resistance $$r = 1 \Omega$$, and an external resistor $$R = 29 \Omega. $$What is the terminal voltage?

$$ V_{terminal} = \varepsilon - Ir $$ where $$I = \frac{\varepsilon}{R + r} $$

Accepted Answer

$$8.7 V $$

Question 15

A parallel circuit has two resistors: $$R_1 = 10$$ \Omega$$ and R_2$ = 20 \Omega. $$What is the total resistance?

$$ \frac{1}{R_{total}} = \frac{1}{R_1$} + \frac{1}{R_2$} $$

Accepted Answer

$$6.67 \Omega$$

Question 16

A lightbulb rated at 60 W, 120 V is connected to a 120 V source. What is the current through the bulb?

$$ P = IV $$

Accepted Answer

$$0.5 A $$

Question 17

A capacitor of $$10 \muF is $$charged to 5 V. How much energy is stored in the capacitor?

$$ U = \frac{1}{2} C V^2$ $$

Accepted Answer

$$1.25 	imes 10$$^{-4}$$ J

Question 18

A circuit contains a resistor ($$R = 100 \Omega) $$and a capacitor ($$C = 50 \muF) in $$series. What is the time constant $$	au$$?

$$ 	au = RC $$

Accepted Answer

$$5.0 s $$

Question 19

A patient monitor uses a resistor of $$2.0 \Omega$$ and a capacitor of $$10 \muF in $$series. If the monitor is powered by a 3 V battery, what is the initial current when the circuit is first connected?

$$ I_0$ = \frac{V}{R} $$

Accepted Answer

$$1.5 A $$

Electric Current, Circuits, and Resistance: Step-by-Step Physics Guidance

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