Ten identical cells connected is series are needed to heated a wire of length one meter and radius 'r'by `10^(@)C` in time t. How many cells will be required to heat the wire of length two meter of the same radius by the same temperature in time 't' ?

Options

A. 10
B. 20
C. 30
D. 40

Answer

B

Explanation

Resistance is directly proportion! to length of the wire. As length is doubled so mass is doubled and resistance is doubled.
We have,
`((10 E)^2)/ ( R) t = mS Delta T`, Now `((n E)^(2) t)/( 2 R)=(2 m ) S Delta T`
`rArr (n^(2) E^(2) t)/( 2 R) = 2 (10^(2) E^(2) t)/( R)`
`rArr n = 20`