For the figure given below which of these sets of E, R and

For the figure given below which of these sets of E, R and C value will ensure that the state equation dV_c / dt = 1.25 V_C + 2 is valid—

1. 2 V, 1 Ω, 1.25 F
2. 1.6 V, 0.8 Ω, 1 F
3. 1.6 V, 1Ω, 0.8 F
4. 2 V, 1.25 Ω, 1 F

We know that current across capacitor is given by the relation

i = C	dv	....(i)
	dt

Applying KVL to the given circuit
E = iR + VC

E = RC	dV_C	+ V_C
	dt

		E	-	V_C	=	dV_C	.....(ii)
		RC		RC		dt

on comparing equation (ii) with the given standard equation

	dV_C	= 1.25 V_C + 2 ....(iii)
	dt

from equations (i), (ii) and (iii), we get

		E	= 2 and	V_C	= 1.25 V_C ⇒ RC =	1_C	.....(ii)
		RC		RC		1.25

E = 2RC = 2 ×	1	= 1.6
	1.25

RC =	1	= 0.8 given in option (B) and (C)
	1.25