1.

The differential equation of charging of a capacitor isas given below: 1/K_1 (dq)/(dt)+K_2q = K_3 The time constant and steady state charge are respectively

Answer»

`1/K_1` and `K_3`
`1/(K_1K_2)` and `K_3/K_2`
`K_2/K_1` and `K_2K_3`
`1/(K_1K_2)` and `K_3/K_1`

Solution :Consider the circuit
`epsilon-Q/C-IR=0`
`I=(dq)/(DT)`
Now, `epsilonC=(dq)/(dt). RC +q`

`rArr RC(dq)/(dt)+q = epsilonC` [where , `q_0=Cepsilon`] …(i)
Comparing EQ. (i) with `1/K_1 . (dq)/(dt) + K_2q = K_3`, we get
`tau=1/(K_1K_2) , q_0 = K_3/K_2`


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