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Network Elements and the Concept of Circuit

Easy Questions

Network Theory

Network Elements and the Concept of Circuit
Network theory miscellaneous
  1. The initial voltage on the capacitor is Vc (0–) = 2 V, I (s) = u (t) cos t find V (t) for t > 0—


    1. V (t) =
      1
      		cos (t – 45º) +
      3
      		e– t
      22
    2. V (t) = 2 cos (t – 45º) +
      3
      		e+ t
      2
    3. V (t) = cos (t – 45º) +
      1
      		e– 2t
      2
    4. V (t) = cos (t + 45º) +
      3
      		e– 2t
      2
Correct Option: A

Here Zeq =
1 .( 1 / Jω)
, ω = 1 on comparing with I (s) = u (t) cos
1 + (1 / Jω)


or Z eq =
1
1 + J

Since initial voltage on the capacitor is V(0–) = 2 V,
so, V (t) J (s), Zeq = cos t.
1
+ A e– st
1 + J

s=
1
 cos (t– 45°) + A e– st given that at t = 0. V (0) = 2 V
√2

so, 2 =
1
 2 cos (0 – 45º) + A e–5.0
√2

2 =
1
√2 + A
√2

or A =
3
2

S =
1
 =
1
 = 1
RC1 x 1

V (t) = cos (t – 45°) +
3
e– t
2


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