NEET Current Electricity: Important Questions, Formulas and Solutions by PW

When you solve Current Electricity questions, you need to know which formula to apply and when. A complicated circuit may become easier once you identify the relationships between current, potential difference and resistance. To avoid common mistakes, you must distinguish between series and parallel combinations, choose the correct cell formula and check the conditions under which each result applies.

Physics Wallah’s important questions break the chapter into focused topics, from the microscopic picture of drift velocity to circuit-level laws and measuring instruments. Use each answer to review the formula, understand its conditions and try the related numerical before moving on.

Current Electricity: Important Questions and Answers

Q1. What Is Electric Current, and How Do You Calculate Charge from a Current-Time Graph?

Electric current is the rate of flow of electric charge through a cross-section of a conductor.

• Instantaneous current: I = dq/dt

• Average current: I(avg) = ΔQ / Δt

• SI unit: ampere (A), where 1 A = 1 C/s

Conventional current flows in the direction of positive charge movement. In a metallic conductor, electrons move opposite to it.

On a charge-time graph, the slope gives current. On a current-time graph, the area under the curve gives charge transferred.

Solved example: The current varies as I = 20t + 8t². Find the charge transferred from t = 0 to t = 15 s.

Q = ∫ (20t + 8t²) dt, from 0 to 15
Q = [10t² + 8t³/3], from 0 to 15
Q = 11250 C

Memory tip: Given charge, differentiate to find current. Given current, integrate to find charge.

Q2. What Is Drift Velocity, and How Is It Related to Electric Current?

Drift velocity is the average velocity gained by charge carriers under an applied electric field. In a metal, electrons drift opposite to the field, while conventional current flows along it.

• v_d = eEτ / m

• I = n e A v_d

• v_d = I / (n e A)

Here e is the electron charge, E the electric field, τ the relaxation time, m the electron mass, n the free-electron number density and A the cross-sectional area.

Use v_d = eEτ/m when E and τ are given. Use v_d = I/(neA) when current, area and number density are known.

Q3. What Are Ohm’s Law, Resistivity and Conductivity?

Ohm’s law: at constant physical conditions, the current through an ohmic conductor is directly proportional to the potential difference across it.

• V = IR

• R = ρL / A

• ρ = m / (n e² τ)

• σ = 1/ρ = n e² τ / m

Units: resistance in ohm (Ω), resistivity in Ω m, conductivity in S/m.

For metals, conductivity generally decreases as temperature rises because greater scattering reduces the relaxation time.

Q4. What Are Mobility and Current Density?

Mobility is the drift velocity per unit electric field.

• μ = v_d / E = eτ / m

• v_d = μE

If the electric field doubles, drift velocity doubles but mobility stays the same.

Current density is the current per unit cross-sectional area.

• J = I / A

• J = n e v_d

• Vector form of Ohm’s law: J = σE, or equivalently E = ρJ

Current density is a vector, directed along conventional current in a metallic conductor.

Q5. How Does the Resistance of a Wire Change When It Is Stretched?

For a uniform conductor, R = ρL/A. When a wire is stretched at constant volume, its length increases and its area decreases.

Volume is constant: A L = A’ L’

If the new length is n times the original, the new area is A/n, so:

R’ = ρ (nL) / (A/n)
R’ = n² R

Solved example: A wire of resistance 4 Ω is stretched to twice its length at constant volume.
R’ = 2² × 4 = 16 Ω

Useful areas:

• Circular wire: A = π r²

• Hollow cylindrical wire: A = π (R² − r²), where R and r are the outer and inner radii

Q6. What Are the Rules for Resistors in Series and Parallel?

In series the same current flows through each resistor. In parallel the potential difference across each branch is the same.

Series

• R(eq) = R₁ + R₂ + R₃ + …

• Voltage drops are proportional to resistance: V₁/V₂ = R₁/R₂

Parallel

• 1/R(eq) = 1/R₁ + 1/R₂ + …

• Branch current: I = V/R

• For two branches: I₁/I₂ = R₂/R₁

The branch with lower resistance carries more current.

Memory tip: Series means same current. Parallel means same potential difference.

Q7. What Are Kirchhoff’s Rules, and How Are They Used in Circuits?

Junction rule: Total current entering a junction equals total current leaving it.
ΣI(in) = ΣI(out) (conservation of charge)

Loop rule: The algebraic sum of potential changes around a closed loop is zero.
ΣΔV = 0

Sign conventions while traversing a loop:

• Battery, negative to positive terminal: +E

• Battery, positive to negative terminal: −E

• Resistor, along the current: −IR

• Resistor, against the current: +IR

An ideal wire has zero resistance, so there is no potential drop along it.

Q8. How Do Ideal Ammeters, Voltmeters and Galvanometers Behave in a Circuit?

• Ideal ammeter: Connected in series, with zero resistance, so it does not change the circuit current.

• Ideal voltmeter: Connected in parallel, with infinite resistance, so it draws no current.

• Galvanometer: Detects small currents. Zero deflection means zero current in its branch.

In ideal-circuit questions, treat an ammeter as a wire and a voltmeter as an open circuit.

Q9. How Do You Calculate the Terminal Voltage of a Cell?

A cell has emf E and internal resistance r.

• Discharging: V = E − Ir

• Charging: V = E + Ir

• Open circuit (I = 0): V = E

• Short circuit (external resistance zero): I(short) = E / r, and the terminal voltage is zero in the ideal model

n identical cells in series

• E(eq) = nE

• r(eq) = nr

n identical cells in parallel

• E(eq) = E

• r(eq) = r/n

m parallel branches, each with n identical cells in series

• E(eq) = nE

• r(eq) = nr/m

Q10. What Are the Formulas for Electrical Power and Joule Heating?

Electrical power is the rate at which electrical energy is transferred or converted.

• P = VI

• P = I²R

• P = V²/R

Joule heating:

• H = I²Rt

• For time-varying current: H = ∫ i² R dt

At constant current, power increases with resistance. At constant voltage, power decreases as resistance increases.

Q11. Which Bulb Glows Brighter in Series and Parallel?

Brightness depends on the power a bulb consumes. For a bulb rated V and P, its resistance is:

R = V² / P

For the same rated voltage, a higher-power bulb has lower resistance.

• In parallel: Each bulb gets the full supply voltage, so the higher-power-rated bulb glows brighter.

• In series: The same current flows through both. Since P = I²R, the bulb with greater resistance (the lower-power-rated one) glows brighter.

These comparisons assume similar bulb ratings and idealised conditions.

Q12. What Is the Principle of a Meter Bridge?

A meter bridge works on the balanced Wheatstone bridge principle. At balance, no current flows through the galvanometer, and the resistance ratio equals the ratio of wire lengths.

If the gap resistances are P and S, and the balance point is at L cm from one end:

P / S = L / (100 − L)

At the balance point, the galvanometer shows zero deflection.

Q13. How Does Resistance Change with Temperature?

For resistance R₀ at 0 °C:

R(T) = R₀ (1 + αT)

where α is the temperature coefficient of resistance and T is in °C.

For a general reference temperature T₀:

R(T) = R(T₀) [1 + α (T − T₀)]

For metals, α is positive, so resistance rises with temperature. For semiconductors and many insulators, resistance usually falls as temperature rises. The linear relation is valid only over a suitable temperature range.

To score well in Current Electricity, match each problem to the right relationship: drift velocity for microscopic questions, series-parallel rules for networks, Kirchhoff’s laws for multi-loop circuits and the power formulas for heating and brightness. Revise the conditions behind each formula, then practise numericals on stretched wires, cell combinations and meter bridges. PW’s topic-wise questions help you build both speed and accuracy for NEET Physics.

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