Consider the LR circuit shown in the figure. If the switch S is closed at t = 0 then the amount of charge that passes through the battery between t = 0 and t = L R is:

Step-by-step solution

The current in the LR circuit at any time t is I = E R 1 - e - R t L Where E ,   R ,   L ,   I are the EMF, resistance, inductance and the current respectively. ∴ Charge flown through the circuit from time 0 to L R is (charge) ∆ q = ∫ 0 L R I . d t = ∫ 0 L R E R 1 - e - R t L d t ⇒ ∆ q = E R t + L R   e - R t L 0 L R ⇒ ∆ q = E R L R + L R e - 1 - L R ⇒ ∆ q = E R × L e R ⇒ ∆ q = E L e R 2 = E L 2.7 R 2