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1. Fundamental Definitions
- Current ($I$): The rate of flow of electric charges. $I = Q / t$. (Unit: Ampere).
- Potential Difference ($V$): Work done to move a unit charge between two points. $V = W / Q$. (Unit: Volt).
2. Ohm's Law
The electric current ($I$) flowing through a metallic wire is directly proportional to the potential difference ($V$) across its ends, provided temperature remains constant.
$$V = I \times R$$
Where $R$ is the constant of proportionality called Resistance (Unit: Ohm, $\Omega$).
3. Combination of Resistors
- Series Circuit: Total resistance $R_s = R_1 + R_2 + R_3$. Current remains the same throughout; voltage is divided.
- Parallel Circuit: $\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$. Voltage remains the same across each resistor; current is divided.
4. Heating Effect & Power
Joule's Law of Heating: $$H = I^2 \times R \times t$$
Electric Power ($P$): $$P = V \times I = I^2 \times R = \frac{V^2}{R}$$
CBSE Board Exam Classic Question
Why are parallel circuits preferred for domestic wiring? If one appliance breaks or is switched off in a series circuit, the entire circuit breaks and everything stops working. In parallel, each appliance operates independently with its own switch, and every appliance receives the full rated voltage.