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Chapter 19: Electromagnetism (Numerical Problems)

Download free solved numericals covering transformer turns ratio formula V_s/V_p = N_s/N_p (secondary voltage / primary voltage = secondary turns / primary turns), step-up transformer (N_s > N_p, increases voltage, decreases current), step-down transformer (N_s < N_p, decreases voltage, increases current), ideal transformer power conservation V_p I_p = V_s I_s (input power = output power), power formula P = VI, efficiency calculations, examples: step-up transformer with 1:100 ratio and 20 V input gives V_s = 2000 V, step-down transformer with 100:1 ratio and 170 V input gives V_s = 1.7 V, 100 W transformer drawing 0.5 A input gives V_p = 200 V, secondary current 8.3 A gives V_s ≈ 12.05 V, turns ratio N_p/N_s ≈ 16.6:1, step-down transformer with 230 V input and 0.050 A gives input power 11.5 W, at 100% efficiency output power 11.5 W, with output voltage 6 V gives secondary current ≈ 1.9 A, adapter stepping up 115 V to 230 V for 5 A load: output power = 1150 W, mains current = 1150/115 = 10 A, and step-up vs step-down identification (step-up: V_s > V_p or N_s > N_p; step-down: V_s < V_p or N_s < N_p) - strictly according to FBISE 2026 SLOs.

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Chapter Overview & SLOs

How do we relate voltage and turns in a transformer? The transformer equation states that the ratio of secondary to primary voltage (V_s/V_p) is equal to the ratio of secondary to primary turns (N_s/N_p). V_s/V_p = N_s/N_p.

What are step-up and step-down transformers?

| Type | Turns Ratio | Voltage | Current | |------|-------------|---------|---------| | Step-up | N_s > N_p | Increases | Decreases | | Step-down | N_s < N_p | Decreases | Increases |

What is the power relationship in an ideal transformer? For a 100% efficient (ideal) transformer, input power equals output power: P_p = P_s, or V_p I_p = V_s I_s. This is derived from the conservation of energy.

What is the power formula? P = V × I, where P is power in watts, V is voltage in volts, I is current in amperes.

Example 1 - Step-up transformer: A step-up transformer with a 1:100 ratio and 20 V input: V_s = V_p × (N_s/N_p) = 20 × 100 = 2000 V.

Example 2 - Step-down transformer: A step-down transformer with a 100:1 ratio and 170 V input: V_s = 170 × (1/100) = 1.7 V.

Example 3 - Finding input voltage from power and current: For a 100 W transformer drawing 0.5 A input, V_p = P/I = 100/0.5 = 200 V. If secondary current is 8.3 A and assuming ideal transformer, V_s = V_p I_p / I_s = (200 × 0.5)/8.3 = 100/8.3 ≈ 12.05 V. Turns ratio N_p/N_s = V_p/V_s = 200/12.05 ≈ 16.6:1.

Example 4 - Step-down transformer with efficiency: A step-down transformer with 230 V input and 0.050 A current: Input power = 230 × 0.050 = 11.5 W. At 100% efficiency, output power = 11.5 W. If output voltage is 6 V, secondary current = 11.5/6 ≈ 1.92 A.

Example 5 - Adapter mains current: An adapter steps up 115 V to 230 V for a 5 A load. Output power = 230 × 5 = 1150 W. At 100% efficiency, input power = 1150 W. Mains current = 1150/115 = 10 A.

Summary of formulas:

| Formula | Description | |---------|-------------| | V_s/V_p = N_s/N_p | Transformer voltage-turns relationship | | V_p I_p = V_s I_s | Ideal transformer power conservation | | P = VI | Electric power | | Step-up | N_s > N_p, V_s > V_p, I_s < I_p | | Step-down | N_s < N_p, V_s < V_p, I_s > I_p |

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

  • How do we calculate the secondary voltage in step-up and step-down transformers? For a step-up transformer with a 1:100 ratio and $20\text{ V}$ input, $V_s = 20 \times 100 = 2000\text{ V}$. Conversely, a step-down transformer with a 100:1 ratio and $170\text{ V}$ input yields $V_s = 170 / 100 = 1.7\text{ V}$.
  • How do we find input voltage and turns ratios from power ratings? For a $100\text{ W}$ transformer drawing $0.5\text{ A}$, the input voltage is $V_p = 100 / 0.5 = 200\text{ V}$. If the secondary current is $8.3\text{ A}$, the secondary voltage is $\approx 12.05\text{ V}$, resulting in a turns ratio $N_p / N_s \approx 16.6:1$.
  • How is output power and current determined for a 100% efficient system? Given a step-down transformer with $230\text{ V}$ input and $0.050\text{ A}$ current, the input power is $11.5\text{ W}$. At 100% efficiency, the output power is also $11.5\text{ W}$; if the output voltage is $6\text{ V}$, the secondary current is $11.5 / 6 \approx 1.9\text{ A}$.
  • How do we calculate the mains current using the power conservation principle? In an adapter stepping up $115\text{ V}$ to $230\text{ V}$ for a $5\text{ A}$ load, the output power is $230 \times 5 = 1150\text{ W}$. The current drawn from the mains is then $1150 / 115 = 10\text{ A}$.

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 19 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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