Electricity involves the flow of electric charge (typically electrons) through conductors. This chapter covers electric charge, potential difference, resistance, Ohm's Law, and the combination of resistors in circuits.
Key Concepts
Electric charge (Q): A fundamental property of matter. Like charges repel; unlike charges attract. SI unit: Coulomb (C).
Electric current (I): The rate of flow of electric charge. I = Q/t. SI unit: Ampere (A). 1 A = 1 C/s. Measured with an ammeter (connected in series).
Electric potential difference (V): The work done per unit charge to move a charge between two points. V = W/Q. SI unit: Volt (V). 1 V = 1 J/C. Measured with a voltmeter (connected in parallel).
Ohm's Law: At constant temperature, the current through a conductor is directly proportional to the potential difference across it: V = IR. (where R = resistance in ohms, symbol omega).
Resistance (R): Opposition to the flow of current. R = V/I. SI unit: Ohm (omega). Factors affecting resistance: length (R proportional to L), cross-sectional area (R inversely proportional to A), material (resistivity rho), temperature.
Resistivity: R = rho x L / A, where rho = resistivity of the material (SI unit: ohm-m).
Series and Parallel Combinations
- Series combination:
- Same current through all resistors.
- Total resistance: Rs = R1 + R2 + R3 + ...
- Voltage divides: V = V1 + V2 + V3
- Parallel combination:
- Same voltage across all resistors.
- Total resistance: 1/Rp = 1/R1 + 1/R2 + 1/R3 + ...
- Current divides: I = I1 + I2 + I3
Heating Effect of Electric Current
Joule's Law of Heating: Heat produced H = I2 x R x t (in Joules). This effect is used in electric heaters, bulbs, fuses, and irons.
Electric Power: P = VI = I2 R = V2/R. SI unit: Watt (W). 1 W = 1 J/s.
Commercial unit of energy: 1 kilowatt-hour (kWh) = 3.6 x 106 J. Also called 1 unit of electricity.
Important Devices
- Fuse: A safety device containing a thin wire with low melting point; breaks the circuit if current exceeds a safe value.
- MCB (Miniature Circuit Breaker): A modern alternative to fuses.
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A charge of 60 C flows through a circuit in 2 minutes. Find the current.
I = Q/t = 60 / (2 x 60) = 60/120 = 0.5 A.
The potential difference between two points is 12 V and the resistance between them is 4 ohms. Find the current using Ohm's Law.
V = IR, so I = V/R = 12/4 = 3 A.
A nichrome wire of length 1 m has a resistance of 10 ohms. Find the resistance of 3 m of the same wire.
Resistance is proportional to length: R2 = R1 x (L2/L1) = 10 x (3/1) = 30 ohms.
Three resistors of 2 ohm, 3 ohm, and 6 ohm are connected in series. Find the total resistance.
Rs = 2 + 3 + 6 = 11 ohms.
The same three resistors (2 ohm, 3 ohm, 6 ohm) are connected in parallel. Find the total resistance.
1/Rp = 1/2 + 1/3 + 1/6 = 3/6 + 2/6 + 1/6 = 6/6 = 1. So Rp = 1 ohm.
An electric iron of resistance 20 ohms draws a current of 5 A. How much heat is produced in 30 seconds?
H = I2 x R x t = 52 x 20 x 30 = 25 x 20 x 30 = 15,000 J = 15 kJ.
An electric bulb is rated 60 W at 220 V. Find (a) the resistance of the bulb and (b) energy consumed in 5 hours.
(a) P = V2/R, so R = V2/P = (220)2 / 60 = 48,400 / 60 approximately 806.7 ohms.
(b) Energy = P x t = 60 W x 5 h = 300 Wh = 0.3 kWh = 0.3 units.
Key Formulas
Key formulas
Common mistakes
Students often confuse series and parallel formulas. In series, resistance adds directly (total is always larger than any individual). In parallel, reciprocals add (total resistance is always less than the smallest resistor). Also remember: the ammeter goes in series; the voltmeter goes in parallel.
Summary
Electric current is the flow of charge; Ohm's Law relates voltage, current, and resistance. Resistors in series add directly; in parallel, their reciprocals add. The heating effect of current (Joule's Law) underpins many household appliances. Electrical power and energy calculations are essential for practical applications.