Key Equations
Electrical Circuits - OCR A-Level Physics
On Data Sheet
Not on Data Sheet
Resistors in Series
$$R_{\text{total}} = R_1 + R_2 + R_3 + \ldots$$
- Where:
- R in ohms ($\Omega$)
Simply add all resistances. Total is always greater than any individual resistor.
Resistors in Parallel
$$\frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \ldots$$
- Where:
- R in ohms ($\Omega$)
Add reciprocals, then take reciprocal of the result. Total is always less than the smallest resistor. For two resistors: R = R_1 R_2 / (R_1 + R_2). On the OCR data sheet.
Potential Divider Output
$$V_{\text{out}} = \frac{R_2}{R_1 + R_2} \times V_{\text{in}}$$
- Where:
- V in volts (V), R in ohms ($\Omega$)
V_out is across R_2. The resistor whose p.d. you want goes in the numerator. Only valid when no current is drawn from the output. On the OCR data sheet.
EMF and Internal Resistance
$$\varepsilon = IR + Ir$$
- Where:
- $\varepsilon$ in volts (V), I in amps (A), R and r in ohms ($\Omega$)
EMF = p.d. across external resistance + p.d. across internal resistance. The 'lost volts' are Ir.
Terminal P.D.
$$V = \varepsilon - Ir$$
- Where:
- V and $\varepsilon$ in volts (V), I in amps (A), r in ohms ($\Omega$)
Terminal p.d. decreases as current increases. When I = 0, V = EMF. This equation gives a straight-line V-I graph with gradient = -r and y-intercept = EMF.