Electricity, Magnetism & Circuits — Problem set, Grade 12

Relate charge, fields, voltage, circuits, induction, stored energy, and electrical power.

Review the key ideas

Electric Charge & Fields

Charge is quantized and conserved; like charges repel and opposites attract with a force given by Coulomb's law F = kq₁q₂/r²; every charge sets up an electric field E = F/q that points away from positive and toward negative charge.

Current, Voltage & Resistance

Current is charge per time; voltage is energy per charge; resistance describes component behavior. For a uniform ohmic wire R=ρL/A under specified conditions.

Circuits & Ohm's Law

Ohm's law V = IR ties voltage, current, and resistance together; series resistances add while parallel resistances give a smaller total (1/R = 1/R₁ + 1/R₂ + …); electrical power is P = IV.

Magnetism & Electromagnetism

Currents produce magnetic fields; forces depend on vector geometry. Changing linked flux induces emf, while a current also requires an appropriate conducting path and energy input.

Electric Potential, Potential Energy & Capacitors

Voltage is energy per charge; capacitors store energy through separated charge.

Electrical Power, Energy & Circuit Design

Compute component power with its own voltage/current and distinguish watts from energy.

Problem 1

Find the force between two 1 μC charges placed 0.1 m apart. (k = 9 × 10⁹ N·m²/C²)
Answer and explanation

0.9 N

F = kq₁q₂/r² = (9 × 10⁹)(1 × 10⁻⁶)(1 × 10⁻⁶) ÷ (0.1)² = (9 × 10⁻³) ÷ 0.01 = 0.9 N. Since the charges have the same sign, the force is repulsive.

Problem 2

A glass rod carries a positive charge and a plastic rod carries a positive charge. Will they attract or repel, and what is the rule?
Answer and explanation

They repel — like charges repel.

Both rods carry the same sign of charge (positive), and the rule for electric charge is that like charges repel while opposite charges attract. So the two positively charged rods push apart.

Problem 3

A 4 μC charge experiences a force of 0.6 N at a point in space. Find the electric field strength at that point.
Answer and explanation

1.5 × 10⁵ N/C (150,000 N/C)

E = F ÷ q = 0.6 ÷ (4 × 10⁻⁶) = 150,000 N/C, or 1.5 × 10⁵ N/C.

Problem 4

A charge of 24 C flows through a wire in 8 seconds. Find the current.
Answer and explanation

3 A

I = Q ÷ t = 24 ÷ 8 = 3 A.

Problem 5

A battery delivers 60 J of energy to 5 C of charge. Find the battery's voltage.
Answer and explanation

12 V

V = W ÷ Q = 60 ÷ 5 = 12 V.

Problem 6

Two wires are identical in every way except that one is twice as long as the other. Which has the greater resistance, and why?
Answer and explanation

The longer wire has the greater resistance.

Resistance increases with length, because charge must push through more material and undergo more collisions. Doubling the length roughly doubles the resistance (R is proportional to length), so the longer wire resists current more.

Problem 7

A 9 V battery is connected to a single 3 Ω resistor. Find the current in the circuit.
Answer and explanation

3 A

By Ohm's law, I = V ÷ R = 9 ÷ 3 = 3 A.

Problem 8

A 2 Ω, a 3 Ω, and a 5 Ω resistor are connected in series to a 20 V battery. Find the total resistance and the current.
Answer and explanation

Total resistance = 10 Ω; current = 2 A

In series, resistances add: R = 2 + 3 + 5 = 10 Ω. Then Ohm's law gives the current: I = V ÷ R = 20 ÷ 10 = 2 A (the same current flows through all three).

Problem 9

Two 6 Ω resistors are connected in parallel. Find their equivalent resistance.
Answer and explanation

3 Ω

1 ÷ R = 1/6 + 1/6 = 2/6 = 1/3, so R = 3 Ω. For two equal resistors in parallel, the total is always half of one.

Problem 10

You move a bar magnet in and out of a coil of wire that is connected to a sensitive meter. Describe what the meter shows and name the effect.
Answer and explanation

The meter shows a current whenever the magnet is moving; this is electromagnetic induction.

While the magnet moves, the magnetic field through the coil is changing, which induces a voltage and drives a current (the needle deflects). Pushing the magnet in and pulling it out send current in opposite directions. When the magnet is held still, the field stops changing and the current stops. This production of current by a changing magnetic field is electromagnetic induction, discovered by Faraday.

Problem 11

A straight wire0.400 m long carries6.00 A perpendicular to a uniform0.300 T field. Find the magnetic-force magnitude.
Answer and explanation

0.72 N

F = BIL = 0.3 × 6 × 0.4 = 0.72 N. This is the force that makes an electric motor's coil turn.

Problem 12

A motor draws a current of 2 A from a 12 V supply. Find its electrical power.
Answer and explanation

24 W

P = IV = 2 × 12 = 24 W.

Problem 13

An electric heater with a resistance of 60 Ω is plugged into a 240 V supply. Find the current it draws and the power it uses.
Answer and explanation

Current = 4 A; power = 960 W

Current: I = V ÷ R = 240 ÷ 60 = 4 A. Power: P = IV = 240 × 4 = 960 W. (You can check with P = V²/R = 240² ÷ 60 = 57,600 ÷ 60 = 960 W.)

Problem 14

A+2microC test charge in 1000N/C field experiences what force?
Answer and explanation

F=qE=.002N along the field; a negative charge would reverse direction.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the calculation or mechanism that supports it.
  • Include units, conditions, or limits where relevant.

Problem 15

Chapter review: A+2 μC test charge in a uniform500 N/C field points east. Find its force. What force acts on a−3 μC test at the same location?
Answer and explanation

F=qE gives+0.0010 N east for+2 μC and−0.0015 N, i.e.west, for−3 μC. The field is unchanged in the ideal nonperturbing-test model.

F=qE gives+0.0010 N east for+2 μC and−0.0015 N, i.e.west, for−3 μC.

The field is unchanged in the ideal nonperturbing-test model.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical or environmental mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

Problem 16

24C passes in 8 s. Find current.
Answer and explanation

I=Q/t=3 A; conventional current direction is positive-charge flow.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the calculation or mechanism that supports it.
  • Include units, conditions, or limits where relevant.

Problem 17

Chapter review: An ohmic12 Ω resistor has9 V across it for40 s. Find current, power and transferred energy.
Answer and explanation

I=9/12=0.75 A; P=VI=6.75 W; E=Pt=270 J. The stated constant resistance and voltage must persist over the interval.

I=9/12=0.75 A; P=VI=6.75 W; E=Pt=270 J.

The stated constant resistance and voltage must persist over the interval.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical or environmental mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

Problem 18

Two 6ohm resistors in parallel have what equivalent R?
Answer and explanation

1/R=1/6+1/6=1/3, soR=3ohm; lower than either branch.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the calculation or mechanism that supports it.
  • Include units, conditions, or limits where relevant.

Problem 19

Chapter review: Two resistors4 Ω and12 Ω are in parallel across an ideal12 V source. Find each current, total current, equivalent resistance and total power.
Answer and explanation

Currents are3 A and1 A; total4 A. Req=12/4=3 Ω and P=12×4=48 W. Branch powers36 W and12 W sum consistently.

Currents are3 A and1 A; total4 A.

Req=12/4=3 Ω and P=12×4=48 W.

Branch powers36 W and12 W sum consistently.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical or environmental mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

Problem 20

What induces emf in a stationary coil?
Answer and explanation

A changing magnetic flux, through changing field, area, or orientation; a moving magnet can supply that change.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the calculation or mechanism that supports it.
  • Include units, conditions, or limits where relevant.

Problem 21

Chapter review: A charge+2 μC moves at3.0×10⁴ m/s perpendicular to a0.20 T field. Find magnetic force magnitude. What happens if velocity becomes parallel to the field?
Answer and explanation

F=|q|vB=0.012 N. Parallel motion gives sin0=0 and zero magnetic-force magnitude in this model; electric forces would need a separate account.

F=|q|vB=0.012 N.

Parallel motion gives sin0=0 and zero magnetic-force magnitude in this model; electric forces would need a separate account.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical or environmental mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

Problem 22

C=.002F,V=5 V. Find stored charge.
Hints

Write the relationship first; substitute with consistent units.

Answer and explanation

0.01 C

Q=CV=.010.

Problem 23

Why is capacitor energy not always QV?
Answer and explanation

Voltage grows during charging; average charging voltage is half final voltage for a linear capacitor.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the calculation or mechanism that supports it.
  • Include units, conditions, or limits where relevant.

Problem 24

Chapter review: A50 μF capacitor is at8 V. Find Q and U; compare U at16 V in the same ideal model.
Answer and explanation

Q=400 μC; U=½×50×10⁻⁶×64=0.0016 J=1.6 mJ. At16 V, U=6.4 mJ, four times as much. Actual ratings must be separately respected.

Q=400 μC; U=½×50×10⁻⁶×64=0.0016 J=1.6 mJ.

At16 V, U=6.4 mJ, four times as much.

Actual ratings must be separately respected.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical or environmental mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

Problem 25

A5W device runs 600 s. Find energy.
Hints

Write the relationship first; substitute with consistent units.

Answer and explanation

3000 J

E=Pt.

Problem 26

Why can a shorted battery overheat?
Answer and explanation

Very low external resistance permits large current; internal resistance then dissipates substantial I²r heat.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the calculation or mechanism that supports it.
  • Include units, conditions, or limits where relevant.

Problem 27

Chapter review: A15 W device is replaced by a9 W device providing the same service for2500 h/year. Find annual energy saved in kWh and joules, and name one uncounted life-cycle term.
Answer and explanation

Saving=(0.015−0.009)×2500=15 kWh=5.40×10⁷ J/year. Production, transport, replacement lifespan or disposal is outside this operational-only result.

Saving=(0.015−0.009)×2500=15 kWh=5.40×10⁷ J/year.

Production, transport, replacement lifespan or disposal is outside this operational-only result.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical or environmental mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.
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