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Question

State whether the following statement is True or False?
In a circuit containing inductance L, resistance R and Voltage E,the current in the circuit is given by LdidtRi=E.The current i at time t is given by i=ER(1eRt/L).

A
True
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B
False
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Solution

The correct option is A True
The given equation
didt+RiL=EL is linear of the type dydxPy=Q.
Its solution is
ie(R/L)dt=e(R/L)dtELdt+c
i.eRt/L=ELeRt/Ldt+c
=ELeRt/LLR+c=EReRt/L+c
when t=0,i=0 =ER
i.eRt/L=ERrRt/LER=ER(eRt/L1)
i=ER(1eRt/L)

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