Electric Current, Potential & Ohm's Law
- Electric Current ($I$): Rate of flow of electric charges through a conductor's cross-section:
$$I = \frac{Q}{t} \quad (\text{SI Unit: Ampere, A})$$
- Electric Potential Difference ($V$): Work done in moving a unit positive charge from one point to another:
$$V = \frac{W}{Q} \quad (\text{SI Unit: Volt, V})$$
Ohm's Law:
At constant temperature, current flowing through a metallic conductor is directly proportional to potential difference across its terminals:
$$V \propto I \implies V = IR$$
Where $R$ is the electrical resistance of the conductor (SI Unit: $\Omega$, Ohm).
Resistance & Resistivity Factors
The resistance $R$ of a uniform conductor depends on:
- Directly proportional to length: $R \propto l$
- Inversely proportional to cross-sectional area: $R \propto \frac{1}{A}$
- Nature of material and temperature:
$$R = \rho \frac{l}{A}$$
Where $\rho$ is the Electrical Resistivity of the material (SI Unit: $\Omega\cdot\text{m}$).
- Conductors have very low resistivity ($10^{-8} - 10^{-6}\,\Omega\cdot\text{m}$).
- Alloys (like Nichrome, Constantan) have higher resistivity and do not oxidize at high temperatures, making them ideal for heating elements.
Combination of Resistors
1. Resistors in Series:
Current remains identical through every resistor; total voltage divides ($V = V_1 + V_2 + V_3$):
$$R_{\text{series}} = R_1 + R_2 + R_3$$
2. Resistors in Parallel:
Voltage across each resistor is identical; total current splits ($I = I_1 + I_2 + I_3$):
$$\frac{1}{R_{\text{parallel}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$$
Heating Effect of Electric Current
Joule's Law of Heating:
Heat produced in a resistor is directly proportional to square of current, resistance, and time:
$$H = I^2Rt = VIt = \frac{V^2}{R}t$$
Electric Power ($P$):
$$P = VI = I^2R = \frac{V^2}{R} \quad (\text{SI Unit: Watt, W})$$
Commercial Unit of Energy:
$$1\text{ kilowatt-hour (kWh)} = 1\text{ unit} = 1000\text{ W} \times 3600\text{ s} = 3.6 \times 10^6\text{ Joules}$$
