Chapter 16: Current Electricity (Numerical Problems)

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Chapter Overview & SLOs

How do we calculate the time required to charge a battery? The charging time is determined by dividing the battery's capacity in Ampere-hours (Ah) by the charging current in Amperes (A). Time = Battery Capacity (Ah) / Charging Current (A).

Example - Battery charging: For a 200 Ah battery connected to a 25 A current, the charging time is Time = 200 / 25 = 8 hours.

What is Ohm's Law? Ohm's Law states that V = IR, where V is voltage (volts), I is current (amperes), and R is resistance (ohms). The current is directly proportional to voltage (I ∝ V) when resistance is constant.

How does changing potential difference affect current? If the potential difference is reduced to one-fourth of its initial value, the current will also decrease to one-fourth, according to the direct proportionality in Ohm's Law (I ∝ V).

What is the resistivity formula? Resistivity ρ = RA/L, where R is resistance (Ω), A is cross-sectional area (m²), L is length (m). The unit of resistivity is ohm-meter (Ω·m).

Important unit conversion for area: 1 mm² = 10⁻⁶ m². When area is given in mm², multiply by 10⁻⁶ to convert to m².

Example - Resistivity calculation: Given R = 0.085 Ω, L = 2 m, A = 0.4 mm² = 0.4 × 10⁻⁶ m². ρ = RA/L = (0.085 × 0.4 × 10⁻⁶)/2 = 1.7 × 10⁻⁸ Ω·m.

What is resistivity as an intrinsic property? Resistivity is an intrinsic property of a material. Stretching a wire to double its length changes its resistance but its resistivity remains the same (unless the material or temperature changes).

What is the temperature coefficient of resistivity? The resistivity of a metallic conductor increases linearly with temperature. Formula: ρT = ρ₀[1 + α(T - T₀)], where ρ₀ is resistivity at reference temperature T₀, α is temperature coefficient of resistivity, and T is final temperature.

Example - Temperature effect on resistivity: For copper wire with ρ₀ = 1.7 × 10⁻⁸ Ω·m, α = 3.9 × 10⁻³ K⁻¹, and temperature increase ΔT = 20 K: ρ = 1.7 × 10⁻⁸ × [1 + (3.9 × 10⁻³ × 20)] = 1.7 × 10⁻⁸ × (1 + 0.078) = 1.7 × 10⁻⁸ × 1.078 = 1.83 × 10⁻⁸ Ω·m.

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

• How is charging time calculated for high-capacity batteries? For a 200 Ah battery connected to a 25 A current, the time is calculated as $\text{Time} = 200\text{ Ah} / 25\text{ A} = 8\text{ hours}$.
• How does changing the potential difference affect the current through a constant resistor? If the potential difference is reduced to one-fourth of its initial value, the current will also decrease to one-fourth, according to the direct proportionality in Ohm's Law ($I \propto V$).
• How do we calculate the resistivity of a wire from its physical dimensions? Given a resistance of 0.085 Ω, a length of 2 m, and a cross-sectional area of 0.4 mm², the resistivity is found using $\rho = RA/L$; converting the area to $0.4 \times 10^{-6}\text{ m}^2$ yields $1.7 \times 10^{-8}\ \Omega\cdot\text{m}$.
• How is the new resistivity calculated after a temperature increase? For a copper wire with an initial resistivity of $1.7 \times 10^{-8}\ \Omega\cdot\text{m}$ and a temperature coefficient $\alpha = 3.9 \times 10^{-3}\text{ K}^{-1}$, a 20 K increase results in a new resistivity of $1.83 \times 10^{-8}\ \Omega\cdot\text{m}$.

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