In an electric circuit, a wire of resistance 10 ohm is used. If this wire is stretched to a length double of its original value, the current in the circuit would become :
- (a)half of its original value.
- (b)double of its original value.
- (c)one-fourth of its original value.
- (d)four times of its original value.
Correct — C, one-fourth of its original value. Stretching a wire keeps its volume constant, so doubling the length halves the cross-sectional area. Since R = rho x L / A, the resistance becomes R' = rho x (2L)/(A/2) = 4R. With the same voltage, the current I = V/R falls to one-quarter (I' = V/4R).
- (a)half of its original value — This assumes R merely doubles; but both the length doubling AND the area halving raise R by a factor of four, so the current drops to a quarter, not a half.
- (b)double of its original value — Stretching increases resistance, which decreases current — it cannot double the current.
- (d)four times of its original value — Resistance rises fourfold, so current falls fourfold; it does not increase.
A wire's resistance is R = rho x L / A. When a wire is stretched, no material is added or removed, so its volume (L x A) stays constant: if the length doubles, the area halves. Because R depends on L/A, resistance scales as the square of the length for a stretched wire — doubling L multiplies R by 4.
Track both changes: L doubles AND A halves, so R goes up 4x. By Ohm's law at constant voltage, current is inversely proportional to resistance, so it drops to 1/4. The 'half' trap forgets the area change.
- Resistance: R = rho L / A.
- Stretching keeps volume (L x A) constant, so doubling L halves A.
- Resistance of a stretched wire scales as length squared: 2x length -> 4x R.
- At constant voltage, current I = V/R falls to one-fourth.
- Forgetting the area halves when the wire is stretched.
- Thinking greater length increases the current.
Asked as the change in resistance/current when a wire is stretched to a multiple of its length.
No directly related past PYQ was found.
- practice — not a real PYQ
A wire is stretched to three times its length. Its resistance becomes
- (a)3 times
- (b)9 times
- (c)1/3
- (d)6 times
Answer(b) 9 times (R scales as length squared).
- practice — not a real PYQ
Resistance of a conductor depends on its length as
- (a)inversely
- (b)directly
- (c)as the square
- (d)not at all
Answer(b) directly (R proportional to L for fixed area).