Question

a wire is cut into several pieces the length and radius of two pieces are in the ratio 1:2 compare the resistance of A and equal and resistance when a and b are connected in parallel

Answer 1

RA​​=13​

Step-by-step explanation:

Hey Mate,


Given,

Two pieces of metal are A and B.

The Ratio of length of pieces A and B is 1 : 2 and ratio of radius of pieces A and B is 1 : 2.

= l_{a} / A_{b} = 1/2la​/Ab​=1/2  and  r_{a} / r_{b} = 1/2ra​/rb​=1/2


we know that R = p\frac{l}{a}R=pal​

where R is resistance, l is length of wire and a is cross sectional area of wire.


so, R_{A} = \frac{l_{A}}{\pi r^{2}_{A} }RA​=πrA2​lA​​ and R_{B} = \frac{l_{B}}{\pi r^{2}_{B} }RB​=πrB2​lB​​


We get,

\frac{R_{A}}{R_{B}}=\frac{l_{A} r^2_{B}}{l_{B}r^2_{A}}RB​RA​​=lB​rA2​lA​rB2​​

= \frac{1*2^2}{2*1^2} = 2=2∗121∗22​=2


when both pieces are connected in parallel.

R_{eq} = \frac{R_{A}R_{B}}{R_{A}+ R_{B}} =\frac{1}{3} R_{A}Req​=RA​+RB​RA​RB​​=31​RA​


So,

\frac{R_{A}}{R_{eq}} = \frac{3}{1}Req​RA​​=13​