Engineering
Physics
AC Circuit Analysis
Question

You are given many resistances, capacitors and inductors. These are connected to a variable DC voltage source (the first two circuits) or an AC voltage source of 50 Hz frequency (the next three circuits) in different ways as shown in Column II. When a current I (steady state for DC rms for AC) flows through the circuit, then corresponding voltage V1 and V2. (indicated in circuits) are related as shown in Column I. Match th two

Column - I Column - II
(A) I 0, V1 is proportional to I
(B) I 0, V2 > V1
(C) V1 = 0, V2 = V
(D) I 0, V2 is proportional to I
 
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Solution

For (p) Insteady state when I = constant

                         VL = 0 = V1

So                    V2 = V

                        Option (C)

For (q) V1 = 0 again as I = constant

                         V2 = V

Also V2 = IR ⇒ Propotional to I.

   Option (B), (C), (D)

For (r) XL = ωL = (100 π) 6 × 10–3 ;1.88 Ω

R = 2Ω

V1 = I XL; V2 = IR

So V2 > V1

V2  I

also V1 ∝ I        Option (A), (B), (D)

For (s) V1 = I XL

V2 = I XC where XC1ωC1061Ω

again V1  I; V2  I, I ≠ 0

Option (A), (B) (D)

For (t) V1 = IR when      R = 1000 Ω

V2 = I XC when X1061 Ω

V2 > V1

V1, V2 ∝ I  and I ≠ 0

Option (A), (B), (D)