What this chapter is about
This chapter introduces the fundamental concepts of current electricity. You learn what electric current is, how it flows through conductors, and what makes it flow. The chapter builds your understanding of electric potential, potential difference, and the relationship between current and voltage.
You study Ohm's law, which connects current, voltage and resistance in a simple mathematical form. The chapter then explores how resistances combine in series and parallel arrangements, and how to calculate equivalent resistance in circuits. These ideas are essential for understanding how electrical devices work in homes and industries.
Finally, you learn about the heating effect of electric current and how to calculate electrical energy and power. By the end, you should be able to analyse simple circuits, calculate current and resistance, and understand how electricity is measured and billed in households.
Key ideas
- Electric current is the rate of flow of electric charge through a conductor; its SI unit is the ampere (A), where 1 A = 1 coulomb per second.
- Potential difference between two points is the work done to move a unit positive charge from one point to another; its SI unit is the volt (V).
- Ohm's law states that the current through a metallic conductor is directly proportional to the potential difference across it, provided temperature remains constant: V = IR.
- Resistance is the property of a conductor that opposes the flow of current; its SI unit is the ohm (Ω).
- The resistance of a conductor depends on its length (directly), cross-sectional area (inversely), the material (resistivity), and temperature.
- In a series combination, the equivalent resistance equals the sum of individual resistances: R = R₁ + R₂ + R₃.
- In a parallel combination, the reciprocal of equivalent resistance equals the sum of reciprocals: 1/R = 1/R₁ + 1/R₂ + 1/R₃.
- Electric power is the rate of doing electrical work: P = VI = I²R = V²/R, measured in watts (W).
Formulas and facts to remember
- Current: I = Q/t, where Q is charge in coulombs and t is time in seconds.
- Potential difference: V = W/Q, where W is work done in joules.
- Ohm's law: V = IR, or equivalently I = V/R and R = V/I.
- Resistance of a wire: R = ρL/A, where ρ is resistivity, L is length, A is cross-sectional area.
- Series resistance: R_total = R₁ + R₂ + R₃ + ...
- Parallel resistance: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃ + ...
- Electric power: P = VI = I²R = V²/R, unit is watt (W).
- Electrical energy: E = Pt = VIt, unit is joule (J); commercial unit is kilowatt-hour (kWh), where 1 kWh = 3.6 × 10⁶ J.
Worked examples
Example 1: Finding current using Ohm's law
A resistor of 20 Ω is connected across a 12 V battery. Find the current flowing through it.
Solution: Using Ohm's law, I = V/R I = 12/20 = 0.6 A
The current through the resistor is 0.6 ampere.
Example 2: Equivalent resistance in a combination circuit
Two resistors of 6 Ω and 3 Ω are connected in parallel. This combination is then connected in series with a 4 Ω resistor. Find the total resistance.
Solution: First, find the parallel combination: 1/R_p = 1/6 + 1/3 = 1/6 + 2/6 = 3/6 = 1/2 R_p = 2 Ω
Now add the series resistor: R_total = R_p + 4 = 2 + 4 = 6 Ω
The total resistance of the circuit is 6 Ω.
Example 3: Calculating electrical energy consumption
A 100 W bulb is used for 5 hours daily. Calculate the energy consumed in 30 days and the cost if electricity costs ₹5 per kWh.
Solution: Daily energy = Power × Time = 100 W × 5 h = 500 Wh = 0.5 kWh Monthly energy = 0.5 × 30 = 15 kWh Cost = 15 × 5 = ₹75
The monthly cost of running the bulb is ₹75.
Common mistakes
- Confusing current with charge → Current is the rate of flow of charge, not charge itself; use I = Q/t.
- Adding resistances in parallel directly → In parallel, add reciprocals first, then take the reciprocal of the sum.
- Forgetting that the same current flows through all components in series → In series circuits, current is constant; voltage divides.
- Mixing up watts and kilowatt-hours → Watt measures power (rate of energy use); kWh measures total energy consumed.
- Using wrong units for resistivity calculations → Ensure length is in metres, area in square metres, and resistivity in Ω·m.
Quick revision
- Current (I) = Charge (Q) ÷ Time (t); unit is ampere.
- Ohm's law: V = IR; valid when temperature is constant.
- Series: same current, resistances add; Parallel: same voltage, reciprocals add.
- Power = Voltage × Current; Energy = Power × Time.
- 1 kWh = 1000 W used for 1 hour = 3.6 × 10⁶ J.
- Resistance increases with length; decreases with thicker wire.