In the circuit in fig. If no current flows through the galvanometer when the key k is closed, the bridge is balanced. The balancing condition for bridge is

Options

A. `(C_1)/(C_2) = (R_1)/(R_2)`
B. `(C_1)/(C_2) = (R_2)/(R_1)`
C. `(C_1^(2))/(C_(2)^(2)) = (R_(1)^(2))/(R_(2)^(2))`
D. `(C_(2)^(1))/(C_(2)^(2))= (R_(2))/(R_(1))`

Answer

B

Explanation

Step I : Switch at position 1: Since circuit is in the steady state, the current through circuit is zero. According to the loop rule,
`E_(0) - (q_(0))/(C_(1)(2R)) = (q_(0)) =C_(0)E_(0)`
Step II : Switch at position 2 : in V this case, the total energy stored in the capacitor appears as heat energy in the resistor. `Delta H = I^(2) RT :. Delta H prop R`
`:. (DeltaH)/(DeltaH_(2)) = (R_(1))/(R_(2)) = (r_(0))/(2r_(0)) = (1)/(2) or Delta H_(2) = 2DeltaH_(1)`
But `Delta H = Delta H_(1) + DeltaH_(2) = (DeltaH_(2))/(2) + DeltaH_(2) = (3)/(2)DeltaH_(2)`
`:. DeltaH_(2) = (2)/(3)DeltaH = (2)/(3)xx(1)/(2)C_(0)E_(0)^(2) = (1)/(3)C_(0)E_(0)^2`