3.7.5.5
UK mains: 230 V means RMS, the peak is 325 V
Alternating Currents — AQA A-Level Physics
- The UK mains supply is rated at 230 V, 50 Hz. Both of these are values you should know for the exam.
- The 230 V is an RMS value. The actual voltageThe energyThe capacity to do work. Measured in joules (J). transferred per unit chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). between two points. Measured in volts (V). Informal term for potential difference. oscillates between +325 V and -325 V, passing through zero 100 times per second.
Working out the peak voltageThe energyThe capacity to do work. Measured in joules (J). transferred per unit chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). between two points. Measured in volts (V). Informal term for potential difference.
- Rearranging $V_{\text{rms}} = V_0 / \sqrt{2}$ gives $V_0 = V_{\text{rms}} \times \sqrt{2}$.
- $V_0 = 230 \times \sqrt{2} = 230 \times 1.414 = 325$ V.
- So the peak-to-peak voltageThe energyThe capacity to do work. Measured in joules (J). transferred per unit chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). between two points. Measured in volts (V). Informal term for potential difference. is 650 V. That's the total swing from maximum positive to maximum negative.
Angular frequencyThe number of complete oscillations passing a point per unit time. Measured in hertz (Hz). of UK mains
- $\omega = 2\pi f = 2\pi \times 50 = 100\pi = 314$ rad s$^{-1}$.
- The full equation for UK mains voltage is: $V = 325 \sin(314t)$, or equivalently $V = 325 \sin(100\pi t)$.
Examiner Tips and Tricks
- If a question says 'the mains supply' without specifying the voltage, use 230 V (RMS) and 50 Hz.
- These are standard values that examiners expect you to know.
- Some older textbooks use 240 V — stick with 230 V for AQA.