Electric Circuits — Practice Quiz

A Physics cheat sheet for Electric Circuits — every key formula with its symbols defined — plus a medium-level practice quiz to test recall.

Formulas & key concepts

Ohm's Law: Voltage \(V\) equals current \(I\) times resistance \(R\).

$$V = IR$$

Resistance: Resistance \(R\) of a wire depends on resistivity \(\rho\), length \(L\), and cross-sectional area \(A\).

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

Electric Power: Power \(P\) dissipated in a resistor or delivered by a source.

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

Series Resistors: Equivalent resistance \(R_S\) is the sum of individual resistances.

$$R_S = R_1 + R_2 + \dots$$

Parallel Resistors: Reciprocal of equivalent resistance \(R_P\) is sum of reciprocals of individual resistances.

$$\frac{1}{R_P} = \frac{1}{R_1} + \frac{1}{R_2} + \dots$$

Terminal Voltage: Voltage across battery terminals equals EMF \(\mathcal{E}\) minus voltage drop across internal resistance \(r\).

$$V_{term} = \mathcal{E} - Ir$$

Series Capacitors: Reciprocal of equivalent capacitance \(C_S\) is sum of reciprocals of individual capacitances.

$$\frac{1}{C_S} = \frac{1}{C_1} + \frac{1}{C_2} + \dots$$

Parallel Capacitors: Equivalent capacitance \(C_P\) is sum of individual capacitances.

$$C_P = C_1 + C_2 + \dots$$

RC Time Constant: Time constant \(\tau\) characterizes the charging/discharging rate of an RC circuit.

$$\tau = RC$$

Capacitor Charging: Charge \(q\) on a capacitor at time \(t\) as it charges towards equilibrium charge \(q_0\).

$$q = q_0 [1 - e^{-t/\tau}]$$

Capacitor Discharging: Charge \(q\) on a capacitor at time \(t\) as it discharges from initial charge \(q_0\).

$$q = q_0 e^{-t/\tau}$$

Practice quiz

  1. A resistor has a resistance of $100 \text{ \Omega}$. If a current of $0.5 \text{ A}$ flows through it, what is the voltage across the resistor?

    • $200 \text{ V}$
    • $50 \text{ V}$
    • $0.005 \text{ V}$
    • $100.5 \text{ V}$

    Answer: $50 \text{ V}$

  2. A copper wire has a resistivity of $1.68 \times 10^{-8} \text{ \Omega} \cdot \text{m}$, a length of $10 \text{ m}$, and a cross-sectional area of $1 \times 10^{-6} \text{ m}^2$. What is its resistance?

    • $1.68 \text{ \Omega}$
    • $0.0168 \text{ \Omega}$
    • $0.168 \text{ \Omega}$
    • $16.8 \text{ \Omega}$

    Answer: $0.168 \text{ \Omega}$

  3. A $12 \text{ V}$ battery is connected to a resistor, and a current of $2 \text{ A}$ flows through it. What is the power dissipated by the resistor?

    • $6 \text{ W}$
    • $24 \text{ W}$
    • $14 \text{ W}$
    • $0.167 \text{ W}$

    Answer: $24 \text{ W}$

  4. Three resistors with resistances $R_1 = 10 \text{ \Omega}$, $R_2 = 20 \text{ \Omega}$, and $R_3 = 30 \text{ \Omega}$ are connected in series. What is their equivalent resistance?

    • $60 \text{ \Omega}$
    • $5 \text{ \Omega}$
    • $0.183 \text{ \Omega}$
    • $20 \text{ \Omega}$

    Answer: $60 \text{ \Omega}$

  5. Two resistors, $R_1 = 6 \text{ \Omega}$ and $R_2 = 3 \text{ \Omega}$, are connected in parallel. What is their equivalent resistance?

    • $9 \text{ \Omega}$
    • $2 \text{ \Omega}$
    • $0.5 \text{ \Omega}$
    • $18 \text{ \Omega}$

    Answer: $2 \text{ \Omega}$

  6. A battery has an EMF of $12 \text{ V}$ and an internal resistance of $0.5 \text{ \Omega}$. If it delivers a current of $2 \text{ A}$ to an external circuit, what is its terminal voltage?

    • $12 \text{ V}$
    • $13 \text{ V}$
    • $11 \text{ V}$
    • $10 \text{ V}$

    Answer: $11 \text{ V}$

  7. Two capacitors, $C_1 = 10 \text{ \mu F}$ and $C_2 = 15 \text{ \mu F}$, are connected in series. What is their equivalent capacitance?

    • $25 \text{ \mu F}$
    • $6 \text{ \mu F}$
    • $0.167 \text{ \mu F}$
    • $150 \text{ \mu F}$

    Answer: $6 \text{ \mu F}$

  8. Three capacitors with capacitances $C_1 = 2 \text{ \mu F}$, $C_2 = 3 \text{ \mu F}$, and $C_3 = 5 \text{ \mu F}$ are connected in parallel. What is their equivalent capacitance?

    • $10 \text{ \mu F}$
    • $0.1 \text{ \mu F}$
    • $1 \text{ \mu F}$
    • $30 \text{ \mu F}$

    Answer: $10 \text{ \mu F}$

  9. An RC circuit has a resistance of $100 \text{ k\Omega}$ and a capacitance of $10 \text{ \mu F}$. What is its time constant?

    • $1000 \text{ s}$
    • $10 \text{ s}$
    • $1 \text{ s}$
    • $0.001 \text{ s}$

    Answer: $1 \text{ s}$

  10. A capacitor with an initial charge $q_0$ is discharging through a resistor. If the RC time constant is $2 \text{ s}$, what percentage of the initial charge remains on the capacitor after $2 \text{ s}$?

    • $100\%$
    • $63.2\%$
    • $36.8\%$
    • $0\%$

    Answer: $36.8\%$

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