Current Electricity

1. Introduction

Current electricity deals with the flow of electric charge through conductors. It forms the basis of circuit analysis and electrical measurements.

2. Electric Current

I = dQ/dt (rate of flow of charge). SI unit: ampere (A).

Current density: J = I/A = σE, where σ is conductivity.

3. Ohm's Law

V = IR (at constant temperature). R = ρL/A, where ρ is resistivity.

4. Resistivity and Conductivity

4.1 Variation with Temperature

ρ = ρ₀[1 + α(T - T₀)], where α is the temperature coefficient.

For metals, ρ increases with temperature. For semiconductors, ρ decreases.

4.2 Color Code for Resistors

First two bands: digits. Third band: multiplier (power of 10). Fourth band: tolerance (gold = 5%, silver = 10%).

5. Electromotive Force (EMF)

The potential difference across the terminals of a cell when no current flows. Terminal voltage: V = E - Ir (during discharge).

6. Kirchhoff's Laws

6.1 Junction Rule (KCL)

The sum of currents entering a junction equals the sum of currents leaving. Based on charge conservation.

6.2 Loop Rule (KVL)

The sum of potential drops around any closed loop is zero. Based on energy conservation.

7. Wheatstone Bridge

A circuit for measuring unknown resistance. Balanced when R₁/R₂ = R₃/R₄ (galvanometer shows zero deflection).

8. Meter Bridge

A practical form of Wheatstone bridge using a 1 m wire. R/S = l₁/(100 - l₁).

9. Potentiometer

A device for measuring EMF without drawing current. E = kl, where k is the potential gradient.

'Potentiometer measures the true EMF because it draws no current at the balance point. A voltmeter always draws some current and measures terminal voltage, not true EMF.'

10. Colour Code for Resistors — Expanded

The colour code (first three bands): Black = 0, Brown = 1, Red = 2, Orange = 3, Yellow = 4, Green = 5, Blue = 6, Violet = 7, Grey = 8, White = 9.

Band 4 multiplier: Black=10⁰, Brown=10¹, Red=10², Orange=10³, Gold=10^{-1}, Silver=10^{-2}. Band 5 tolerance: Brown=±1%, Red=±2%, Gold=±5%, Silver=±10%, None=±20%.

Example: Yellow-Violet-Orange-Gold = 47 × 10³ Ω ± 5% = 47 kΩ ± 5%.

11. Potentiometer — Detailed Working

A potentiometer consists of a long uniform wire (usually 10 m) of high resistance connected to a driver cell. The potential gradient k = V/L (V per unit length).

11.1 Comparison of EMFs

E₁ = kl₁, E₂ = kl₂ ⇒ E₁/E₂ = l₁/l₂

11.2 Determination of Internal Resistance

With cell in circuit: V = kl₁ (with resistance R across cell terminals). Without external resistance: E = kl₂. Internal resistance: r = (E/V - 1)R = (l₂/l₁ - 1)R.

'Potentiometer gives the true EMF because at the balance point, no current flows through the cell. This is its key advantage over a voltmeter.'

12. Worked Problems

Problem 1: A wire of resistivity 1.6×10^{-8} Ωm has length 1 m and area 0.5 mm². Find resistance. Solution: R = ρL/A = 1.6×10^{-8} × 1/(0.5×10^{-6}) = 0.032 Ω.

Problem 2: A cell of EMF 2V and internal resistance 0.5Ω is connected to a 4.5Ω resistor. Find current and terminal voltage. Solution: I = E/(R + r) = 2/(4.5 + 0.5) = 0.4 A. V = E - Ir = 2 - 0.4×0.5 = 1.8 V.

Problem 3: Using Kirchhoff's laws, find currents in a network with three loops. Solution: Apply KVL to each loop, KCL at junctions. Solve the linear equations simultaneously.

11. Common Mistakes

'Students often get the sign wrong in loop equations. Moving from negative to positive terminal of a battery gives a positive voltage rise.'

'In complex circuits, always mark current directions and stay consistent with your sign convention throughout.'

12. ISC Exam Focus

13. Self-Test Questions

1. Find the resistance of a copper wire of length 2 m and diameter 0.5 mm (ρ = 1.7×10^{-8} Ωm).
2. A cell of EMF 1.5V gives a current of 0.3A through a 4Ω resistor. Find internal resistance.
3. State and explain Kirchhoff's laws with a suitable diagram.
4. Explain the working of a potentiometer to compare EMFs of two cells.
5. In a meter bridge experiment, the balance point is at 40 cm with a standard resistance of 10 Ω. Find the unknown resistance.