The phase difference between the alternating current and voltage represented by the following equation $I = I_{0} sin ω t, E = E_{0} cos (ω t + \frac{π}{3}),$ will be

\frac{π}{6}

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\frac{π}{3}

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\frac{π}{2}

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\frac{5 π}{6}

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Solution

The correct option is D $\frac{5 π}{6}$
To solve such question, we need to convert the two functions into either $sin$ or $cos$ for comparison.

$I = I_{0} sin ω t$

$E = E_{0} cos (ω t + \frac{π}{3})$

$E = E_{0} sin [\frac{π}{2} + (ω t + \frac{π}{3})]$

$[∵ sin (90 + θ) = cos θ]$

$E = E_{0} sin (ω t + \frac{5 π}{6})$

Clearly, the phase difference, $Δ ϕ = \frac{5 π}{6}$

Hence, option $(D)$ is the correct answer.

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List-I	List- II
(a) Phase difference between current and voltage in a purely resistive AC circuit	(i) π/2; current leads voltage
(b) Phase difference between current and voltage in a pure inductive AC circuit	(ii) zero
(c) Phase difference between current and voltage in a pure capacitive AC circuit	(iii) π/2; current lags voltage
(d) Phase difference between current and voltage in an LCR series circuit	(iv) ${tan}^{- 1} (\frac{X_{C} - X_{L}}{R})$

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