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Chapter 17: Electric Circuits (Numerical Problems)

Download free solved numericals covering equivalent resistance for parallel combination (1/R_e = 1/R₁ + 1/R₂ + 1/R₃), series combination (R_e = R₁ + R₂ + R₃), series-parallel networks, Ohm's Law (I = V/R), current distribution in parallel circuits (current divides among branches, voltage same across all branches), power formula P = V²/R (power consumed by device), electrical energy E = P × t (Watt-hours Wh), EMF of cells in series (total EMF = sum of individual EMFs, e.g., 100 cells of 0.2V each in series gives 20 V), EMF of cells in parallel (total EMF remains same as one cell, e.g., 0.2 V), examples: 12V battery with three devices (6 Ω, 10 Ω, 18 Ω) in parallel gives currents 2 A, 1.2 A, 0.67 A respectively, complex series-parallel network (4 Ω in series with parallel branch of 6 Ω and 5 Ω: parallel branch = 2.73 Ω, total R = 6.73 Ω), 50 Ω bulb on 120 V source gives power P = 288 W, energy consumed in 5 hours = 1440 Wh, and reciprocal calculation in parallel resistance (if 1/R_total = 19/72, then R_total = 72/19 ≈ 3.789 Ω) - strictly according to FBISE 2026 SLOs.

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Chapter Overview & SLOs

How is the total resistance calculated for resistors in parallel? For a parallel combination, the reciprocal of the equivalent resistance (R_e) is the sum of the reciprocals of individual resistances: 1/R_e = 1/R₁ + 1/R₂ + 1/R₃.

How is the total resistance calculated for resistors in series? For a series combination, the equivalent resistance is the sum of individual resistances: R_e = R₁ + R₂ + R₃.

What is Ohm's Law? Ohm's Law states that V = IR, or rearranged, I = V/R, where I is current (amperes), V is voltage (volts), and R is resistance (ohms).

How is current distributed in a parallel circuit? In parallel circuits, the voltage across each branch remains the same as the source voltage, while the current divides among the branches according to Ohm's Law: I = V/R for each branch.

Example - Current in parallel branches: For a 12V battery with three devices of 6 Ω, 10 Ω, and 18 Ω in parallel: I₁ = 12/6 = 2 A, I₂ = 12/10 = 1.2 A, I₃ = 12/18 = 0.67 A.

What formula relates power to voltage and resistance? Electrical power (P) consumed by a device is calculated using P = V²/R, where V is voltage and R is resistance. Also P = IV and P = I²R.

Example - Power calculation: For a 50 Ω bulb connected to a 120 V source, power P = (120)²/50 = 14400/50 = 288 W.

How is electrical energy calculated? Electrical energy (E) is the product of power and time: E = P × t, typically measured in Watt-hours (Wh) or kilowatt-hours (kWh). 1 kWh = 1000 Wh.

Example - Energy calculation: A 288 W bulb used for 5 hours consumes E = 288 × 5 = 1440 Wh = 1.44 kWh.

How do we calculate equivalent resistance for complex series-parallel networks? Simplify parallel branches first, then add series components.

Example - Series-parallel network: A 4 Ω resistor in series with a parallel branch of 6 Ω and 5 Ω. First, find parallel equivalent: 1/R_parallel = 1/6 + 1/5 = (5+6)/30 = 11/30, so R_parallel = 30/11 = 2.73 Ω. Then total resistance R_total = 4 + 2.73 = 6.73 Ω.

What is the resultant EMF when multiple identical cells are combined?

  • Cells in series: Total EMF = sum of individual EMFs. For 100 cells of 0.2 V each, total EMF = 20 V.
  • Cells in parallel: Total EMF remains the same as one cell (0.2 V).

Important note for parallel resistance calculations: After summing the reciprocals, you must take the reciprocal of the result. For example, if 1/R_total = 19/72, then R_total = 72/19 ≈ 3.789 Ω.

These notes are strictly aligned with the Student Learning Outcomes (SLOs) for the FBISE 2026 annual examination.

  • How do we find the current passing through individual devices in a parallel circuit? Given a 12V battery and three devices (6 Ω, 10 Ω, and 18 Ω) in parallel, the current in each is found by $I = V/R$, resulting in 2 A, 1.2 A, and 0.67 A respectively.
  • How is the equivalent resistance calculated for a complex series-parallel network? In a circuit where a 4 Ω resistor is in series with a parallel branch (6 Ω and 5 Ω), the parallel portion is first simplified to 2.73 Ω, making the total resistance 6.73 Ω.
  • What is the resultant EMF when multiple identical cells are combined? When 100 cells of 0.2V each are in series, their EMFs add up to 20 V; if connected in parallel, the total EMF remains 0.2 V.
  • How do we calculate the total energy and power for a high-resistance device? For a 50 Ω bulb connected to a 120V source, the power consumed is 288 W ($P = V^2/R$), and if used for 5 hours, the total electrical energy consumed is 1440 Wh.

Frequently Asked Questions (FAQ)

1. Are these Class 10 Physics notes based on the latest FBISE syllabus for 2026?
Yes, these notes are strictly designed according to the Student Learning Outcomes (SLO) provided by the Federal Board (FBISE) for the 2026 academic year. We regularly update our content to match the latest curriculum changes and exam patterns.

2. Do these Physics 17 notes include solved exercise questions and diagrams?
Absolutely. These notes contain comprehensive solutions to all textbook exercise questions, including Multiple Choice Questions (MCQs), Short Questions, and detailed Long Questions. We also include labeled diagrams and key definitions to help you secure maximum marks in your board exams.

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