A uniformly wound long solenoid of inductance `L` and resistance `R` is cut into two parts in the ratio `eta:1`, which are then connected in parallel. The combination is then connected to a cell of emf `E`. The time constant of the circuit is

Options

A. `L/R`
B. `L/((eta+1)R)`
C. `(eta/(n+1))L/R`
D. `((eta+1)/eta)L/R`

Answer

A

Explanation

`L_1=(eta/(eta+1))L,R_1=(eta/(eta+1))R`
`L_2=(1/(eta+1))L,R_2=(1/(eta+1))R`
`L_("net")=(L_1L_2)/(L_1+L_2)`
Similarly, `R_("net")=(R_1R_2)/(R_1+R_2)`
`tau_L=L_("net")/R_("net")=L/R`