Key Equations
Alternating Currents — AQA A-Level Physics
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RMS voltage
$$V_{\text{rms}} = \frac{V_0}{\sqrt{2}}$$
- Where:
- $V_{\text{rms}}$ = RMS voltage (V)
- $V_0$ = peak voltage (V)
The DC voltage that would give the same power dissipation. 1/√2 ≈ 0.707. Applies to sinusoidal AC only.
Instantaneous AC voltage
$$V = V_0 \sin(\omega t)$$
- Where:
- $V$ = instantaneous voltage (V)
- $V_0$ = peak voltage (V)
- $\omega$ = angular frequency (rad s⁻¹)
- $t$ = time (s)
Assumes V = 0 at t = 0. ω = 2πf. Calculator must be in radians.
RMS current
$$I_{\text{rms}} = \frac{I_0}{\sqrt{2}}$$
- Where:
- $I_{\text{rms}}$ = RMS current (A)
- $I_0$ = peak current (A)
Same factor as RMS voltage. The DC current that would produce the same heating in a resistor.
Mean power (RMS form)
$$P_{\text{mean}} = I_{\text{rms}} V_{\text{rms}}$$
- Where:
- $P_{\text{mean}}$ = mean power dissipated (W)
- $I_{\text{rms}}$ = RMS current (A)
- $V_{\text{rms}}$ = RMS voltage (V)
Standard P = IV but using RMS values. Also valid: P = I_rms²R and P = V_rms²/R.
Angular frequency
$$\omega = 2\pi f$$
- Where:
- $\omega$ = angular frequency (rad s⁻¹)
- $f$ = frequency (Hz)
Connects frequency to the sin(ωt) equations. Also used in SHM and circular motion.
Mean power (peak form)
$$P_{\text{mean}} = \frac{I_0 V_0}{2}$$
- Where:
- $P_{\text{mean}}$ = mean power dissipated (W)
- $I_0$ = peak current (A)
- $V_0$ = peak voltage (V)
Mean power is half the peak power. The factor of 2 comes from (1/√2) × (1/√2) = 1/2.