A cricuite contains an inductance L, a resistance R and a battery of emf E. The circulit is switched on at `t=0` . The change flows through the battery in one time constant `(tau)` is-

Options

A. `(2Etau)/(Re)`
B. `(Etau)/(2Re)`
C. `(Etau)/(Re)`
D. zero

Answer

3

Explanation

At any time t, the circuit grown in accordnce with formula
`I = I_(0) (1 -e ^(-Rt//L))= I_(0)(1 -e^(-t//tau))`
`rArr I=(E)/(R)(1-e^(t//tau))rArr (dq)/(dt)= (E)/(R) (1-e^(-t//tau))`
`rArrdp=(E)/(R) dt-(E)/(R) e^(-t//tau)dt`
`q=(E)/(R)underset(0)overset(tau)int dt -(E)/(R) underset(0)overset(tau)int e^(-t//tau)dt`
`rArr q=(Etau)/(R) -[-(Etau)/(Re)+(Etau)/(R)] =(Etau)/(Re)`