Question 1

The electric potential along the x-axis is given by $$V = 100e$$^{-x^2}$$ - 2xV_0$$, where $$x is in $$meters. What is the magnitude and direction of the electric field at $$x = 1.0 m$$?

Accepted Answer

$$E = 200e$$^{-1}$$ + 2V_0 to $$the left

Question 2

Three capacitors of $$2\mu F$$, $$1\mu F$$, and $$3\mu F$$ are connected as shown in the image (2 and 1 in series, then in parallel with 3). What is the equivalent capacitance?

Accepted Answer

$$C_{eq} = 3.67\mu F$$

Question 3

A $$1.5 V $$battery provides $$0.52 A of $$current to a charge escalator. At what rate is charge lifted by the escalator?

Accepted Answer

$$0.52 C/s$$

Question 4

A $$1.9-m-$$long gold wire has a diameter of $$0.70 mm. $$What is its resistance at $$20^{\circ}C$$? (Resistivity of gold $$ho = 2.44 	imes 10$$^{-8}$$\ \Omega\cdot m)$$

Accepted Answer

$$R = 0.19\ \Omega$$

Question 5

For what electric field strength would the current in a $$2.4-mm-$$diameter nichrome wire be the same as the current in a $$1.2-mm-$$diameter aluminum wire in which the electric field strength is $$0.0068 V/m$$? (Conductivities: $$\sigma_{Ni} = 6.7 	imes 10^5$ S/m, $$\sigma_{Al} = 3.5 	imes $$10^7 S/m)$$

Accepted Answer

$$E_{Ni} = 0.0356 V/m$$

Question 6

The resistivity of copper increases with temperature as $$ho = \$$rho_0$$[1 + \alpha(T - T_0$)]. If a $$copper wire has a resistance of $$0.25\ \Omega at$$ $$20^{\circ}C$$, at what temperature will its resistance be $$0.20\ \Omega$$? ($$\alpha = 3.9 	imes 10$$^{-3}$$\ ^{\circ}C$^{-1})$$

Accepted Answer

$$T = -51$$^{\circ}$$C

Question 7

Three charged particles are placed at the corners of an equilateral triangle with edge length $$2.0 cm. $$One particle has charge $$+3.5 nC$$, a second has $$+7.0 nC. $$What must be the third charge so that the electric potential energy of the three-particle system is zero?

Accepted Answer

$$-3.5 nC$$

Question 8

What is the electric potential at the point indicated by the dot in the center of the triangle formed by charges $$1.0 nC$$, $$2.0 nC$$, and $$-2.0 nC$$, each at $$3.0 cm $$from the center?

Accepted Answer

$$V = 299 V$$

Question 9

Three capacitors with values $$C$$, $$2C$$, and $$3C$$ are connected in series to a battery of voltage $$\Delta V. $$What is the equivalent capacitance $$C_{eq}$$?

Accepted Answer

$$C_{eq} = \frac{1}{\frac{1}{C} + \frac{1}{2C} + \frac{1}{3C}}$$

Question 10

If the voltage across the first capacitor ($$C) in a $$series of $$C$$, $$2C$$, $$3C is$$ $$\frac{1}{6}\Delta V$$, what is the voltage across the third capacitor ($$3C$$)?

Accepted Answer

$$\frac{1}{3}\Delta V$$

Question 11

In a parallel combination of capacitors ($$C$$, $$2C$$, $$3C) $$connected to a battery of voltage $$\Delta V$$, what is the total charge stored on all capacitors?

Accepted Answer

$$Q_{tot} = 6C\Delta V$$

Question 12

Three capacitors $$C_1 = 6.00$$\mu F$$, C_2$ = 3.00\mu F$$, $$C_3 = 5.00$$\mu F$$ are connected as shown and a potential V$$_{ab}$$ is applied. If the charge on C_2$ is 40.0$$\mu C$$, what is the applied voltage V$$_{ab}$$?

Accepted Answer

$$V_{ab} = 13.3 V$$

Question 13

Four wires made of the same material and diameter carry currents $$I_1 to$$ $$I_4 as $$shown. Rank the currents from largest to smallest.

Accepted Answer

$$I_1$$ \u003e $$I_3$$ \u003e $$I_2$$ \u003e $$I_4$$

Question 14

Both batteries in the circuit are ideal and identical, and all bulbs are the same. Rank the brightness of bulbs A, B, and C from brightest to least bright.

Accepted Answer

A \u003e B \u003e C

Question 15

A battery is connected to a $$5.0\Omega$$ and $$10.0\Omega$$ resistor in series. The open-circuit current is $$1.636 A$$, and the closed-circuit current is $$1.565 A. $$What is the emf of the battery?

Accepted Answer

$$\epsilon = 24.8 V$$

Question 16

A switch has been in position 1 for a long time, then is moved to position 2 at $$t=0. $$The battery voltage is $$6 V$$, the capacitor is $$4\mu F$$, and the resistor is $$25\Omega. $$What is the charge $$Q on $$the capacitor immediately after the switch is closed?

Accepted Answer

$$Q = 24\mu C$$

Question 17

A $$40.0\Omega$$ resistor is discharged through a capacitor. The discharge current decreases to $$28\% of $$its initial value in $$2.00 ms. $$What is the value of the capacitor?

Accepted Answer

$$C = 0.025 mF$$

Question 18

In the circuit with $$5\Omega$$, $$4\Omega$$, $$6\Omega$$, and $$10\Omega$$ resistors and a $$24 V $$battery, what is the current through the $$10\Omega$$ resistor?

Accepted Answer

$$I = 1.6 A$$

Question 19

In the circuit with two batteries ($$12 V $$and $$9 V) $$and three resistors ($$5\Omega$$, $$10\Omega$$, $$5\Omega$$), what is the direction of current through the $$10\Omega$$ resistor?

Accepted Answer

Left to right

Physics Study Guide: Electric Circuits, Capacitors, and Electric Potential

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