Electric current is the rate of flow of electric charge through a cross-section. I = dQ/dt. Its SI unit is the Ampere (A = C/s). Conventional current flows from high to low potential (opposite to electron flow).
Key Concepts
- Drift Velocity (vd): The average velocity of free electrons in a conductor under an applied electric field. I = n e A vd, where n = number density of free electrons, e = charge of electron, A = cross-sectional area.
- Ohm's Law: The current through a conductor is directly proportional to the potential difference across it, provided physical conditions (temperature, etc.) remain constant. V = IR.
- Resistance: R = V/I. Its SI unit is Ohm (Omega). For a conductor: R = rho L / A, where rho is resistivity, L is length, A is area.
- Resistivity (rho): Depends on the material and temperature. For metals, rho increases with temperature: rho(T) = rho0 [1 + alpha (T - T0)], where alpha is the temperature coefficient of resistance.
- Conductance and Conductivity: G = 1/R (in Siemens), sigma = 1/rho.
- Kirchhoff's Laws:
- KCL (Junction Rule): The sum of currents entering a junction equals the sum leaving it (charge conservation).
- KVL (Loop Rule): The algebraic sum of potential differences around any closed loop is zero (energy conservation).
- Series combination of resistors: Req = R1 + R2 + R3 ... (same current through all)
- Parallel combination: 1/Req = 1/R1 + 1/R2 + 1/R3 ... (same voltage across all)
- EMF and Internal Resistance: A real cell has EMF (epsilon) and internal resistance r. Terminal voltage V = epsilon - Ir (during discharge).
- Wheatstone Bridge: A circuit for accurate measurement of resistance. Balance condition: P/Q = R/S.
- Potentiometer: An instrument to measure EMF and potential difference without drawing current. Principle: V proportional to length.
- Key Formulas
- I = nAevd; R = rho L/A
- V = epsilon - Ir (terminal voltage)
- Power: P = VI = I2 R = V2/R
- Wheatstone balance: P/Q = R/S
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A copper wire of length 2 m and cross-section 2 × 10-6 m2 has resistivity 1.7 × 10-8 Omega·m. Find its resistance.
R = rho L / A = (1.7 × 10-8 × 2) / (2 × 10-6) = 3.4 × 10-8 / 2 × 10-6 = 0.017 Omega
A cell of EMF 2 V and internal resistance 0.5 Omega is connected to an external resistance of 3.5 Omega. Find the current and terminal voltage.
I = epsilon / (R + r) = 2 / (3.5 + 0.5) = 2/4 = 0.5 A
Vterminal = epsilon - Ir = 2 - 0.5 × 0.5 = 2 - 0.25 = 1.75 V
Find the equivalent resistance of 6 Omega and 3 Omega in parallel.
1/Req = 1/6 + 1/3 = 1/6 + 2/6 = 3/6 = 1/2; Req = 2 Omega
Three resistors 2 Omega, 3 Omega, 5 Omega are in series connected to 10 V. Find the current and power dissipated in 3 Omega.
Rtotal = 2 + 3 + 5 = 10 Omega; I = 10/10 = 1 A
P3 = I2 R = 12 × 3 = 3 W
Apply KVL to a loop with EMF epsilon = 6 V, r = 1 Omega, R1 = 2 Omega, R2 = 3 Omega in series. Find current.
Total resistance = r + R1 + R2 = 1 + 2 + 3 = 6 Omega
I = epsilon / Rtotal = 6/6 = 1 A
KVL check: 6 - 1×1 - 1×2 - 1×3 = 6 - 6 = 0. Verified.
In a Wheatstone bridge, P = 10 Omega, Q = 20 Omega, R = 30 Omega. Find the unknown resistance S for balance.
P/Q = R/S => 10/20 = 30/S => S = 30 × 20/10 = 60 Omega
The resistance of a wire at 20°C is 20 Omega. If alpha = 0.004 /°C, find resistance at 80°C.
R = R0 [1 + alpha (T - T0)] = 20 [1 + 0.004 × (80 - 20)] = 20 [1 + 0.24] = 20 × 1.24 = 24.8 Omega
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Common mistakes
- Confusing EMF (the open-circuit voltage of a cell) with terminal voltage (which is less when current flows due to internal resistance).
- In parallel circuits, the equivalent resistance is always less than the smallest individual resistance.
- When applying KVL, choose a direction for current and be consistent with sign conventions for voltage drops.
Summary
Current electricity covers charge flow, resistance, Ohm's law, and network analysis using Kirchhoff's laws. Understanding EMF, terminal voltage, the Wheatstone bridge, and the potentiometer provides tools for practical circuit analysis and measurement.