Current Electricity – JEE Mains Physics

1. Electric Current: Drift Velocity and Mobility

Electric current is the flow of electric charge, usually through conductors like wires. The drift velocity is the average velocity of charge carriers due to the applied electric field.
The mobility of charge carriers relates the drift velocity to the applied electric field and is given by:
```
v_d = μE
```
where v_d is the drift velocity, μ is the mobility, and E is the electric field.

Ohm's law states that the current (I) through a conductor is directly proportional to the potential difference (V) across it and inversely proportional to its resistance (R):
```
V = IR
```
where V is the voltage, I is the current, and R is the resistance.
Electrical resistance is a measure of the opposition to current flow and is given by:
```
R = ρ (L/A)
```
where ρ is the resistivity, L is the length, and A is the cross-sectional area of the conductor.

For an Ohmic conductor, the current is directly proportional to the voltage, and its I-V graph is a straight line.
Non-ohmic conductors do not follow Ohm's law, and their I-V characteristics may be nonlinear (e.g., for a diode, the current increases exponentially with voltage).

The electrical energy (E) consumed by a device is given by the product of voltage, current, and time:
```
E = VIt
```
The electrical power (P) is the rate at which energy is consumed:
```
P = VI
```

Resistivity (ρ) is a material property that determines how much a material resists the flow of electric current.
Conductivity (σ) is the reciprocal of resistivity and represents how well a material allows current to pass through it:
```
σ = 1/ρ
```

In series, the total resistance (R_total) is the sum of individual resistances:
```
R_total = R₁ + R₂ + ...
```
In parallel, the total resistance is given by the reciprocal sum of the individual resistances:
```
1/R_total = 1/R₁ + 1/R₂ + ...
```

The resistance of most materials increases with temperature. The temperature dependence is given by:
```
R(T) = R₀ [1 + α(T - T₀)]
```
where α is the temperature coefficient of resistance, and T₀ is the reference temperature.

A cell has an internal resistance (r) that causes a voltage drop when a current flows through it.
The potential difference across the terminals of a cell is less than its emf due to this internal resistance.

In series, the emf of the combined cells adds up, but the internal resistance also increases.
In parallel, the emf remains the same, but the equivalent internal resistance decreases.

Kirchhoff’s current law (KCL) states that the total current entering a junction equals the total current leaving the junction.
Kirchhoff’s voltage law (KVL) states that the sum of potential differences (voltage) around any closed loop is zero.

The Wheatstone bridge is used to measure unknown resistance by balancing two legs of a bridge circuit.
The Metre Bridge is a practical implementation of the Wheatstone bridge for measuring resistances in laboratory setups.