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Question

You are given many resistors, 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 or rms for AC) flows through the circuit, the corresponding voltages V1 and V2 (indicated in circuits) are related as shown in Column I. Match the two columns.   Column I   Column II
i I0,V1 is proportional to I a
ii I0,V2>V1 b
iii V1=0,V2=V c
iv I0,V2 is proportional to I d
    e

  1. i - c,d,e ; ii - b,c,d,e ; iii - a,b ; iv - b,c,d,e
  2. i - c,d,e ; ii - b,c,e ; iii - a,b ; iv - b,c,d,e
  3. i - c,d ; ii - b,d,e ; iii - a,b ; iv - b,d,e
  4. i - c,e ; ii - b,c,d,e ; iii - a,b ; iv - b,c,e


Solution

The correct option is A i - c,d,e ; ii - b,c,d,e ; iii - a,b ; iv - b,c,d,e
(a) In this case, steady state current is zero (I=0) because of the presence of capacitor. Entire potential will be across capacitor in steady state. Hence V1=0 and V2=V .

(b) In steady state V1=0, so V2=V. Also V2 is proportional to I.

(c) XL=ωL=2πfL=2π×50×6×103=1.885Ω
    R = 2Ω
since R>XL, so V2>V1
Here I0
V1 and V2 both are proportional to I

(d)  XL=1.885Ω
XC=1ωC=12πfC
=12π×50×3×106=1061Ω
Hence XC>XL, so V2>V1

(e) XC=1.061kΩ,R=1kΩ
XC>R, so V2>V1

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