The diagram shows the variation of V and I in an AC circuit. The circuit only be a series RC or series RL or series LC or series RLC. Consider the four different combinations of V and I graphs. Pick the correct combination/combinations for each graph. Solid curves represent I and broken curves represent V. Take the angular frequency of the AC voltage source to be 100 rad/s. (I) : R = 1kΩ, L = 1H and C = 100μF (II) : R = 1Ω and L = 10–2H (III) : R = 100Ω and C = 10+2μF (IV) : L = 1H and C = 100μF, R = 1Ω

Engineering

Physics

Straight Line Motion

Question

The diagram shows the variation of V and I in an AC circuit. The circuit only be a series RC or series RL or series LC or series RLC. Consider the four different combinations of V and I graphs. Pick the correct combination/combinations for each graph. Solid curves represent I and broken curves represent V.

Take the angular frequency of the AC voltage source to be 100 rad/s.

(I) : R = 1kΩ, L = 1H and C = 100μF (II) : R = 1Ω and L = 10^–2H
(III) : R = 100Ω and C = 10⁺²μF (IV) : L = 1H and C = 100μF, R = 1Ω

a → II ; d → I, IV ;

c → I ; d → none

a → II,III ; b → II,III

b → III ; c → IV

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IV should have been : L = 1H and C = 100μF, R = 1 $Ω$ then answer would have been B & C
V leads I by π/4   inductive (R–L)
R = ωL ⇒ $ω = \frac{R}{L}$
V lags I by π/4    capacitive (R–C)
      $R = \frac{1}{ωC} \Rightarrow ω = \frac{1}{RC}$
V & I are in same phase X_L = X_C ⇒   $ω = \frac{1}{\sqrt{LC}}$
Not possible in R, L, C

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