Task Sets: Ohm's Law - OpenStax Physics (High School)

A

Recall / Warm-Up

1.

Electric current $I$ is defined as:

A.

The rate of charge flow: $I = \Delta Q / \Delta t$

B.

The energy transferred per unit charge: $I = W / Q$

C.

The opposition to charge flow through a material.

D.

The potential difference between two points: $I = V_A - V_B$

2.

Conventional current in a circuit flows in which direction?

A.

From the positive terminal to the negative terminal (from high to low potential).

B.

From the negative terminal to the positive terminal (from low to high potential).

C.

In the same direction as electron flow.

D.

Conventional current has no defined direction — it depends on the circuit.

3.

Which statement about electrical resistance is correct?

A.

Resistance is the opposition to current flow; it converts electrical energy to heat.

B.

Resistance drives current — higher resistance means more current.

C.

Resistance is the same as voltage.

D.

Resistance only exists in insulators, not in conductors.

B

Fluency Practice

1.

A charge of $\Delta Q = 15\ \text{C}$ flows through a wire in $\Delta t = 5.0\ \text{s}$ . What is the current in the wire?

2.

A 9.0 V battery is connected to a resistor of $R = 150\ \Omega$ . What current flows through the resistor?

3.

A current of $I = 2.5\ \text{A}$ flows through a resistor, and the voltage across it is $V = 15\ \text{V}$ . What is the resistance of the resistor?

4.

A resistor has $R = 20\ \Omega$ and carries a current of $I = 0.50\ \text{A}$ . What voltage appears across it?

A.

$10\ \text{V}$

B.

$0.025\ \text{V}$

C.

$40\ \text{V}$

D.

$2.5\ \text{V}$

C

Mixed Practice

D

Word Problems

1.

A phone charging cable carries a current of $I = 1.5\ \text{A}$ for $\Delta t = 45\ \text{min}$ .

How much charge (in coulombs) flows through the cable during this time?

2.

A heating element in a toaster has resistance $R = 24\ \Omega$ and is connected to a household outlet supplying $V = 120\ \text{V}$ .

1.

What current flows through the heating element?

2.

If the resistance of the heating element increases to $R' = 30\ \Omega$ after it heats up (due to increased temperature), what is the new current?

E

Error Analysis

1.

Student's explanation:

"In a circuit with a battery and two resistors in series, the voltage starts at 12 V at the battery. The first resistor uses up some of the voltage, say 5 V worth. The second resistor uses up the remaining 7 V. By the time current gets back to the battery, the voltage has been used up completely — that's why the battery has to keep making more voltage."

A student describes how voltage works in a circuit. Read their explanation and identify the error.

A.

The student is wrong that voltage drops across resistors — voltage is constant everywhere in a circuit.

B.

The student is right that voltage drops across resistors (5 V + 7 V = 12 V is correct) but wrong that voltage is "used up." Voltage is a potential difference — it describes two points in the circuit, not something that flows and gets consumed.

C.

The student is wrong about the numbers — the voltage drops should not add up to the battery voltage.

D.

The entire explanation is correct — voltage is indeed a substance that flows and gets used up.

2.

Student's reasoning:

"I replaced the $20\ \Omega$ resistor with a $100\ \Omega$ resistor in the same circuit (same 12 V battery). Since resistance drives current, the larger resistance will push more current through the circuit. I calculate the new current as $I = R \times V = 100 \times 12 = 1200\ \text{A}$ ."

A student analyzes a circuit and makes a claim. Read their reasoning and find the mistake.

A.

The student used the correct formula but made an arithmetic error.

B.

The student used $I = R \times V$ instead of $I = V/R$ , and has the physical reasoning backwards — resistance limits current, not drives it.

C.

The student is right that larger resistance drives more current — the only error is the calculation.

D.

The student's formula and reasoning are both correct.

F

Challenge

1.

Explain in physical terms (using the electron-collision model) why the resistance of a metal wire increases when its temperature increases, but the resistance of a thermistor (semiconductor) decreases when its temperature increases. What does this tell you about the different physical mechanisms in metals vs. semiconductors?

2.

A V-I graph for a non-ohmic device shows the following data points: at $V = 2\ \text{V}$ , $I = 0.10\ \text{A}$ ; at $V = 6\ \text{V}$ , $I = 0.20\ \text{A}$ .

1.

Calculate the resistance at each operating point. At $V = 2\ \text{V}$ : $R =$ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ $\Omega$ . At $V = 6\ \text{V}$ : $R =$ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ $\Omega$ .

R at V=2V (Ω):

R at V=6V (Ω):

2.