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Resistance and Resistivity

Electrical power and energy in resistive circuits

  • 3 things to know
  • Unit AS 1

Overview

Recall questions on P = VI and the derivations of P = I²R and P = V²/R, the factor of four when current doubles, calculating energy transferred over a time, why transmission is at high voltage, which of two resistors dissipates more in series and in parallel, and why a fuse melts.

What you need to know

Answer each one before you reveal it.

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Key term

State the equation for the power dissipated in a resistor in terms of current and resistance, and define every symbol.

Key term

State the equation for the power dissipated in a resistor in terms of potential difference and resistance.

Numbers

A current of 3.0 A flows through an 8.0 Ω resistor for 2.0 minutes. Calculate the energy dissipated.

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    State the equation for the power dissipated in a resistor in terms of current and resistance, and define every symbol.

    Model answer

    The equation is P = I²R, where P is the power in watts, I the current in amperes and R the resistance in ohms.

  2. 2

    Show how P = I²R follows from P = VI.

    Model answer

    For a resistor V = IR, so substituting into P = VI gives P = (IR)I = I²R.

  3. 3

    State the equation for the power dissipated in a resistor in terms of potential difference and resistance.

    Model answer

    The power is P = V²/R, obtained by substituting I = V/R into P = VI, where V is in volts and R in ohms.

  4. 4

    Calculate the power dissipated when a current of 2.0 A flows through a 15 Ω resistor.

    Model answer

    The power is P = I²R = 2.0² × 15 = 60 W, and 60 W ÷ 2.0 A gives 30 V, which is indeed 2.0 A × 15 Ω, confirming the result.

  5. 5

    Calculate the power dissipated in a 6.0 Ω resistor with a potential difference of 12 V across it.

    Model answer

    The power is P = V²/R = 144 ÷ 6.0 = 24 W, and the current is 2.0 A so P = VI = 12 × 2.0 = 24 W, confirming the result.

  6. 6

    A heater is rated at 1.2 kW when connected to a 230 V supply. Calculate the resistance of its element.

    Model answer

    The resistance is R = V²/P = 52 900 ÷ 1200 = 44 Ω, and 230² ÷ 44.1 returns 1.2 × 10³ W as a check.

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