5.1.4 Circuits

1. Series and Parallel Resistors

• Series Connection: The total resistance, $R_T$ , is the sum of the individual resistances.

$$R_T = R_1 + R_2 + R_3 + \dots$$

• Parallel Connection: The reciprocal of the total resistance is the sum of the reciprocals of the individual resistances.

$$\frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \dots$$

2. Power and Energy Transfer in Circuits

• Power ($P$) is the rate of energy transfer. It is calculated using:

$$P = \frac{E}{t} \quad \text{or} \quad P = VI \quad \text{or} \quad P = I^2 R \quad \text{or} \quad P = \frac{V^2}{R}$$

where $E$ is the energy transferred, $V$ is the potential difference, $I$ is the current, and $R$ is the resistance.

• Energy Transferred (E):

$$E = VIt$$

3. Series and Parallel Circuits – Current and Voltage Distribution

• Series Circuits:
  • The current is the same throughout the circuit.
  • The total potential difference (p.d.) across the circuit is the sum of the potential differences across each component.

• Parallel Circuits:
  • The total current is the sum of the currents through each branch.
  • The potential difference across each branch is the same.

4. Battery Cells in Series and Parallel

• When connected in series, the total voltage is the sum of each cell's voltage.

$$V_T = V_1 + V_2 + V_3 + \dots$$

• When identical cells are connected in parallel, the total voltage remains the same as a single cell's voltage.

5. Kirchhoff's Laws

• Kirchhoff's First Law: The total current flowing into a junction is equal to the total current flowing out. This is based on conservation of charge.
• Kirchhoff's Second Law: In any closed loop within a circuit, the sum of the electromotive forces (e.m.f.s) is equal to the sum of the potential drops. This law follows the conservation of energy.