Phasors and Phasor Diagrams

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Question

An R-C series circuit is connected to an alternating source of emf $V = V_{0} \cos 100 πt$ , instantaneous current in the circuit is $i = 5 \cos (100 πt + \frac{π}{4}) A,$ the value of $V_{0}$ is [Resistance R used in the circuit is $10 Ω$ ]

Moderate

Solution

$\begin{array}{l} \frac{X_{C}}{R} = \tan 45^{o} \Rightarrow X_{C} = R \Rightarrow Z = \sqrt{R^{2} + {X_{C}}^{2}} = \sqrt{2} R = 10 \sqrt{2} Ω \\ ∴ \frac{V_{0}}{Z} = 5 \Rightarrow V_{0} = 5 \times 10 \sqrt{2} Volt = 50 \sqrt{2} Volt \end{array}$

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Similar Questions

The diagram shows a capacitor C and a resistor R connected in series to an ac source. V₁ and V₂ are voltmeters and A is an ammeter

Consider now the following statements
I. Readings in A and $V_{2}$ are always in phase
II. Reading in $V_{1}$ is ahead in phase with reading in $V_{2}$
III. Readings in A and $V_{1}$ are always in phase

Which of these statements are/is correct

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