Q: During the charging of a capacitor in an RC circuit, which equation correctly describes the charge on the capacitor as a function of time?

$$Q(t) = Q_0$ (1 - e$$^{-t/\tau}$$)$$

Q: A $$5\,\mu F$$ capacitor is charged to $$10\,V. $$How much energy is stored in the capacitor?

$$U = 2.5 \times 10$$^{-5}$$\,J$$

Question 1

Which statement best describes the function of Electromotive Force (EMF) in a battery?

Accepted Answer

EMF is the influence that makes current flow from low potential to high potential inside the battery, converting chemical energy to electrical energy.

Question 2

A battery with EMF $$\varepsilon$$ does $$W$$ joules of work to move a charge $$q. $$What is the correct formula for the work done by the battery?

Accepted Answer

$$W = q \varepsilon$$

Question 3

In a circuit, you cross a resistor in the direction of current flow. What happens to the electric potential and what is the correct expression for the change?

Accepted Answer

The potential decreases by $$IR$$; $$\Delta V = -IR$$

Question 4

Which of the following is Kirchhoff's Junction Rule?

Accepted Answer

The current that flows into a junction is the same as the current that flows out.

Question 5

Three resistors $$R_1 = 10$$\,\Omega$$, R_2$ = 20\,\Omega$$, and $$R_3 = 30$$\,\Omega$$ are connected in series. What is the equivalent resistance?

Accepted Answer

$$R_{eq} = 60\,\Omega$$

Question 6

Two resistors $$R_1 = 6$$\,\Omega$$ and R_2$ = 3\,\Omega$$ are connected in parallel. What is the equivalent resistance?

Accepted Answer

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

Question 7

In a parallel circuit, which quantity is the same across all resistors?

Accepted Answer

Voltage drop

Question 8

A circuit contains a battery of $$\varepsilon = 12\,V$$ and two resistors $$R_1 = 4$$\,\Omega$$ and R_2$ = 8\,\Omega in $$series. What is the current in the circuit?

Accepted Answer

$$I = 12/12 = 1\,A$$

Question 9

A $$10\,\mu F$$ capacitor is charged to $$5\,V$$ and then discharged through a $$2\,k\Omega$$ resistor. What is the time constant $$	au$$ for this circuit?

Accepted Answer

$$	au = 0.01\,s$$

Question 10

During the charging of a capacitor in an RC circuit, which equation correctly describes the charge on the capacitor as a function of time?

Accepted Answer

$$Q(t) = Q_0$ (1 - e$$^{-t/	au}$$)$$

Question 11

A capacitor is discharging through a resistor. At time $$t = 	au$$, what fraction of its initial charge remains?

Accepted Answer

$$1/e$$

Question 12

In a multi-loop circuit, what is the correct procedure to solve for unknown currents?

Accepted Answer

Assign polarity to EMF sources, assign currents to branches, apply Kirchhoff's rules, and solve for unknowns.

Question 13

A $$100\,\Omega$$ resistor and a $$200\,\Omega$$ resistor are connected in parallel. What is the equivalent resistance?

Accepted Answer

$$R_{eq} = 66.7\,\Omega$$

Question 14

A $$5\,\mu F$$ capacitor is charged to $$10\,V. $$How much energy is stored in the capacitor?

Accepted Answer

$$U = 2.5 	imes 10$$^{-5}$$\,J$$

Question 15

In a circuit, the sum of the voltage drops around a closed loop is zero. This is an example of:

Accepted Answer

Kirchhoff's Loop Rule

Question 16

A $$10\,\Omega$$ resistor and a $$20\,\Omega$$ resistor are connected in series to a $$12\,V$$ battery. What is the power dissipated by the $$20\,\Omega$$ resistor?

Accepted Answer

$$P = 3.2\,W$$

Question 17

A capacitor in an RC circuit is charged to $$V_0. At $$what time $$t is $$the energy stored in the capacitor half of its initial value?

Accepted Answer

$$t = 	au \ln \sqrt{2}$$

Question 18

Which equation correctly gives the equivalent resistance for $$n$$ resistors in parallel?

Accepted Answer

$$\frac{1}{R_{eq}} = \sum_{i=1}^n \frac{1}{R_i}$$

DC Circuits: EMF, Resistors, Kirchhoff's Rules, and RC Circuits

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