Water jacketed copper rod ‘D’ m in diameter is used to carry the current. The water, which flows continuously maintains the rod temperature at T0i C during Normal operation at ‘I’ amps. The electrical resistance of the rod is known to be ‘R’ W/M. If the coolant water ceased to be available and the heat removal diminished greatly, the rod would eventually melt. Water is the time required for melting to occur if the melting point of the rod material is Tmp? (Cp= specific heat, r density of the rod material and L is the length of the rod). (IES-95)
a.$\rho \left ( \frac{\pi D^2}{4} \right )C_p\frac{(T_{mp}-T_i)}{I^2R}$
b.$\frac{(T_{mp}-T_i)}{\rho I^2R}$
c.$\rho \frac{(T_{mp}-T_i)}{I^2}$
d.$C_p\frac{(T_{mp}-T_i)}{I^2R}$