Cliste School
Get started

Electricity & Magnetism

Current Electricity

5th Year · 6th Year (Leaving Cert)

  • ✓Define and apply Ohm's Law to calculate voltage, current, and resistance in simple circuits.
  • ✓Analyse and calculate total resistance, current, and voltage in series and parallel circuits.
  • ✓Explain the concepts of electromotive force (EMF) and internal resistance of a power source.
  • ✓Calculate the terminal voltage of a power source considering its internal resistance.
  • ✓Apply the formulae for electrical power (P = IV, P = I²R, P = V²/R) to solve problems.

Key concepts

Ohm's Law

Ohm's Law states that for a metallic conductor at constant temperature, the potential difference (voltage) across it is directly proportional to the current flowing through it. The constant of proportionality is the resistance (R) of the conductor.

V = IR
Resistance

Resistance is a measure of how much a material opposes the flow of electric current. It is measured in ohms (Ω).

R = V/I
Series Circuits

In a series circuit, components are connected end-to-end, forming a single path for the current. The current is the same through all components (I_total = I_1 = I_2 = ...). The total voltage is the sum of the voltages across each component (V_total = V_1 + V_2 + ...). The total resistance is the sum of individual resistances (R_total = R_1 + R_2 + ...).

R_total = R_1 + R_2 + ...
Parallel Circuits

In a parallel circuit, components are connected across the same two points, providing multiple paths for the current. The total current is the sum of the currents through each branch (I_total = I_1 + I_2 + ...). The voltage is the same across all components (V_total = V_1 = V_2 = ...). The reciprocal of the total resistance is the sum of the reciprocals of individual resistances (1/R_total = 1/R_1 + 1/R_2 + ...).

1/R_total = 1/R_1 + 1/R_2 + ...
Electromotive Force (EMF)

EMF (E) is the total energy supplied per unit charge by a power source (e.g., battery) when no current is flowing or when the circuit is open. It is the maximum potential difference a source can provide. Measured in volts (V).

Internal Resistance (r)

All real power sources have some internal resistance due to the materials they are made from. When current flows, some of the EMF is 'lost' as a voltage drop across this internal resistance.

Terminal Voltage (V)

The terminal voltage is the actual potential difference across the terminals of a power source when current is flowing. It is less than the EMF due to the voltage drop across the internal resistance.

V = E - Ir
Electrical Power

Electrical power is the rate at which electrical energy is converted into other forms of energy (e.g., heat, light). It is measured in watts (W).

P = IV = I²R = V²/R

Key facts to remember

  • 1Ohm's Law: V = IR, where V is potential difference, I is current, and R is resistance.
  • 2In a series circuit, current is constant, voltages add (V_total = ΣV), and resistances add (R_total = ΣR).
  • 3In a parallel circuit, voltage is constant, currents add (I_total = ΣI), and reciprocals of resistances add (1/R_total = Σ(1/R)).
  • 4EMF (E) is the maximum potential difference a source can provide; terminal voltage (V) is the actual voltage across the terminals when current flows.
  • 5Internal resistance (r) causes a voltage drop (Ir) within the source, so V = E - Ir.
  • 6Electrical power can be calculated using P = IV, P = I²R, or P = V²/R.
  • 7The unit of resistance is the ohm (Ω), and the unit of power is the watt (W).

Worked examples

Example 1

A 12 V battery is connected to two resistors, 4 Ω and 8 Ω, in series. Calculate (a) the total resistance, (b) the total current flowing in the circuit, and (c) the voltage across the 4 Ω resistor.

I(a) For resistors in series, R_total = R_1 + R_2.
IIR_total = 4 Ω + 8 Ω = 12 Ω.
III(b) Using Ohm's Law, I = V / R_total.
IVI = 12 V / 12 Ω = 1 A.
V(c) The current through each resistor in a series circuit is the same (1 A). Using Ohm's Law for the 4 Ω resistor, V_4Ω = I × R_4Ω.
VIV_4Ω = 1 A × 4 Ω = 4 V.

Answer

(a) 12 Ω, (b) 1 A, (c) 4 V

Example 2

Two resistors, 6 Ω and 12 Ω, are connected in parallel across a 24 V power supply. Calculate (a) the total resistance of the parallel combination, (b) the total current drawn from the supply, and (c) the power dissipated in the 6 Ω resistor.

I(a) For resistors in parallel, 1/R_total = 1/R_1 + 1/R_2.
II1/R_total = 1/6 Ω + 1/12 Ω = 2/12 Ω + 1/12 Ω = 3/12 Ω = 1/4 Ω.
IIIR_total = 4 Ω.
IV(b) Using Ohm's Law, I_total = V / R_total.
VI_total = 24 V / 4 Ω = 6 A.
VI(c) In a parallel circuit, the voltage across each branch is the same as the supply voltage, so V_6Ω = 24 V.
VIIUsing the power formula P = V²/R for the 6 Ω resistor:
VIIIP_6Ω = (24 V)² / 6 Ω = 576 V² / 6 Ω = 96 W.

Answer

(a) 4 Ω, (b) 6 A, (c) 96 W

Remember that the voltage is the same across parallel components.

Example 3

A battery has an EMF of 1.5 V and an internal resistance of 0.5 Ω. It is connected to an external resistor of 2.5 Ω. Calculate (a) the total current flowing in the circuit, (b) the terminal voltage of the battery, and (c) the power dissipated in the external resistor.

I(a) The total resistance in the circuit is the sum of the external resistance and the internal resistance: R_total = R_external + r.
IIR_total = 2.5 Ω + 0.5 Ω = 3.0 Ω.
IIIThe total current is given by I = E / R_total.
IVI = 1.5 V / 3.0 Ω = 0.5 A.
V(b) The terminal voltage (V) is given by V = E - Ir.
VIV = 1.5 V - (0.5 A × 0.5 Ω) = 1.5 V - 0.25 V = 1.25 V.
VIIAlternatively, V = I × R_external = 0.5 A × 2.5 Ω = 1.25 V.
VIII(c) The power dissipated in the external resistor can be calculated using P = I²R.
9P_external = (0.5 A)² × 2.5 Ω = 0.25 A² × 2.5 Ω = 0.625 W.

Answer

(a) 0.5 A, (b) 1.25 V, (c) 0.625 W

The terminal voltage is always less than the EMF when current is flowing.

Common mistakes

  • ✗Confusing the rules for calculating total resistance in series and parallel circuits.
  • ✗Incorrectly assuming EMF and terminal voltage are always the same.
  • ✗Forgetting to include internal resistance in total resistance calculations when applicable.
  • ✗Mixing up current and voltage values when applying Ohm's Law or power formulae in complex circuits.
  • ✗Not converting units (e.g., mA to A, kΩ to Ω) before calculations.

Exam tips

  • ★Always draw a clear circuit diagram and label all known values (V, I, R, E, r) before starting calculations.
  • ★Show all steps in your calculations, including formulae used, substitutions, and units in the final answer.
  • ★Pay close attention to whether resistors are in series or parallel, as this dictates the rules for current, voltage, and resistance.
  • ★When dealing with EMF and internal resistance, remember that the total resistance of the circuit includes the internal resistance of the source.

Ready to practise?

Try a problem on this topic

Snap a photo or type a question — get step-by-step working instantly.

Solve a problem →← Physics curriculum