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 :
- $R =\frac{2 \rho}{\pi l} \ln \left(\frac{ b }{ a }\right)$
- $R =\frac{\rho}{\pi l} \ln \left(\frac{ b }{ a }\right)$
- $R =\frac{\rho}{2 \pi l}\left(\frac{ b }{ a }\right)$
- $R =\frac{\rho}{2 \pi l} \ln \left(\frac{ b }{ a }\right)$
The Correct Option is D
Solution and Explanation
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Concepts Used:
Current Electricity
Current electricity is defined as the flow of electrons from one section of the circuit to another.
Types of Current Electricity
There are two types of current electricity as follows:
Direct Current
The current electricity whose direction remains the same is known as direct current. Direct current is defined by the constant flow of electrons from a region of high electron density to a region of low electron density. DC is used in many household appliances and applications that involve a battery.
Alternating Current
The current electricity that is bidirectional and keeps changing the direction of the charge flow is known as alternating current. The bi-directionality is caused by a sinusoidally varying current and voltage that reverses directions, creating a periodic back-and-forth motion for the current. The electrical outlets at our homes and industries are supplied with alternating current.