Conductivity σ = 1/ρ where ρ is resistivity. Since resistivity is in Ω·m, conductivity is in (Ω·m)⁻¹ = S/m or mho/meter.
Q.2Easy
A copper wire and an aluminum wire of the same length and cross-sectional area carry the same current. Which wire has greater power dissipation?
Answer: B
Resistivity of aluminum (2.65 × 10⁻⁸ Ω·m) is greater than copper (1.68 × 10⁻⁸ Ω·m). Since P = I²R and R = ρL/A, aluminum has higher resistance and thus higher power dissipation for same current.
Q.3Medium
In a balanced Wheatstone bridge, if the resistance of one arm is changed by 10%, by what percentage should another arm be changed to maintain balance?
Answer: A
For Wheatstone bridge: P/Q = R/S. If P increases by 10%, then Q must also increase by 10% to maintain the ratio and balance condition.
Q.4Easy
The drift velocity of electrons in a copper wire is approximately:
Answer: B
Drift velocity vd = I/(nAe) is typically 10⁻⁴ to 10⁻³ m/s for normal currents, much slower than thermal velocity (~10⁶ m/s) but much slower than light speed.
Q.5Easy
Two resistances R₁ and R₂ are connected in parallel. If R₁ = 4Ω and R₂ = 6Ω, what is the equivalent resistance?
A metallic conductor's resistance increases with temperature. This is primarily because:
Answer: B
As temperature increases, atoms vibrate more vigorously, increasing collision frequency with drifting electrons. This increases mean free path reduction and thus resistance increases.
Q.11Medium
A heating element rated 1000W, 200V is connected to a 100V supply. The heat generated will be:
Answer: A
Resistance R = V²/P = (200)²/1000 = 40Ω (constant). Heat at 100V: P = V²/R = (100)²/40 = 4010000 = 250W.
Q.12Medium
In a meter bridge, the null point is found at 60cm from left. If a standard resistance of 15Ω is on the right, the unknown resistance is:
Answer: A
In meter bridge: R/S = l₁/l₂ where l₁ = 60cm, l₂ = 40cm. R/15 = 4060 = 23 → R = 15 × 23 = 22.5Ω.
Q.13Hard
The sensitivity of a galvanometer can be increased by:
Answer: D
Sensitivity θ ∝ NAB/k. It increases with more turns (N) and weaker torsional constant (k). Both B and C increase sensitivity.
Q.14Hard
A wire of length L and cross-sectional area A has resistance R. If the wire is stretched to length 2L without change in volume, the new resistance will be:
Answer: B
When stretched, volume constant: A × L = A' × 2L → A' = A/2. New resistance R' = ρ(2L)/(A/2) = 4ρL/A = 4R.
Q.15Easy
The EMF of a cell is 1.5V. When a current of 2A is drawn, the terminal voltage is 1.2V. The internal resistance is:
Answer: A
E = V + Ir → 1.5 = 1.2 + 2r → 0.3 = 2r → r = 0.15Ω.
Q.16Medium
A copper wire of diameter 1 mm carries a current of 5 A. If the drift velocity of electrons is 0.5 mm/s, find the number density of free electrons in copper. (Given: e = 1.6 × 10⁻¹⁹ C)
Answer: A
Using I = nAve, where n is number density. A = π(0.5×10⁻³)². Solving gives n = 8.05 × 10²⁸ m⁻³
Q.17Easy
Two wires of the same material have lengths in ratio 2:3 and diameters in ratio 1:2. Their resistances are in the ratio?
In a Wheatstone bridge, if the four resistances are P, Q, R, and S connected in order, and the galvanometer shows zero deflection, which condition is satisfied?
Answer: D
At null deflection: P/Q = R/S, which is equivalent to P·S = Q·R. Both are valid balanced bridge conditions
Q.19Easy
An ideal ammeter connected in series with a circuit has resistance of:
Answer: C
An ideal ammeter must have zero resistance to not affect the circuit current. In practice, ammeters have very low resistance (mΩ range)
Q.20Medium
A potential divider uses a 100 cm wire of total resistance 10Ω. A cell of EMF 2V and negligible internal resistance is connected across it. What is the potential gradient along the wire?
