JEE PYQ: Current Electricity Question 19
Question 19 - 2020 (03 Sep 2020 Shift 1)
Model a torch battery of length $l$ to be made up of a thin cylindrical bar of radius ‘$a$’ and a concentric thin cylindrical shell of radius ‘$b$’ filled in between with an electrolyte of resistivity $\rho$ (see figure). If the battery is connected to a resistance of value $R$, the maximum Joule heating in $R$ will take place for:
(1) $R = \frac{\rho}{2\pi l} \left(\frac{b}{a}\right)$
(2) $R = \frac{\rho}{2\pi l} \ln\left(\frac{b}{a}\right)$
(3) $R = \frac{\rho}{\pi l} \ln\left(\frac{b}{a}\right)$
(4) $R = \frac{2\rho}{\pi l} \ln\left(\frac{b}{a}\right)$
Show Answer
Answer: (2)
Solution
Maximum power in external resistance when $R = r$ (internal resistance). $dR = \frac{\rho,dr}{2\pi r l}$, $R = \int_a^b \frac{\rho}{2\pi l} \frac{dr}{r} = \frac{\rho}{2\pi l} \ln\frac{b}{a}$.
BETA
