Question : Two wires P and Q are made of the same material. The wire Q has twice the diameter and half the length as that of wire P. If the resistance of wire P is R, the resistance of the wire Q will be
(A) R
(B) R/2
(C) R/8
(D) 2R
CBSE 2025
Solution : Both the wire have same material i.e. Resistivity (ρ) remains same.
RP=R
RQ=?
LP=L
dP=d
LQ=L/2
dQ=2d
We know,
R=ρL/A
R=ρL/πd²
R∝L/d²
RQ/RP=[LQ/d²Q]/[LP/d²P]
RQ/RP=[LQ/LP]×[dP/dQ]²
RQ/RP=[LQ/LP]×[dP/dQ]²
RQ/R=[(L/2)/L]×[d/2d]²
RQ/R=[1/2]×[1/2]²
RQ/R=[1/2]×[1/4]
RQ/R=[1/8]
RQ=R/8
Hence, (C) R/8, would be the correct option.
RQ=?
LP=L
dP=d
LQ=L/2
dQ=2d
We know,
R=ρL/A
R=ρL/πd²
R∝L/d²
RQ/RP=[LQ/d²Q]/[LP/d²P]
RQ/RP=[LQ/LP]×[dP/dQ]²
RQ/RP=[LQ/LP]×[dP/dQ]²
RQ/R=[(L/2)/L]×[d/2d]²
RQ/R=[1/2]×[1/2]²
RQ/R=[1/2]×[1/4]
RQ/R=[1/8]
RQ=R/8
Hence, (C) R/8, would be the correct option.
