SATHEE: alternating-currents Question 15

alternating-currents Question 15

Question: Q. 3. The power factor of an $a c$ circuit is 0.5 . What is the phase difference between voltage and current in the circuit?

A [O.D. I, 2016]

[Topper’s Answer 2016]

Short Answer Type Questions-1

(2 marks each)

Q. 1. An alternating voltage $E = E_{0} \sin ω t$ is applied to the circuit containing a resistor $R$ connected in series with a black box. The current in the circuit is found to be $I = I_{0} \sin (ω t + \frac{π}{4})$

(i) State whether the element in the black box is a capacitor or inductor.

(ii) Draw the corresponding phasor diagram and find the impedance in terms of $R$ .

U[ [CBSE SQP 2017-18]

Show Answer

Solution:

Ans. (i) As the current leads the voltage by $\frac{π}{4}$ , the element used in black box is a ‘capacitor’.

(ii) Phasor diagram :

$\tan \frac{π}{4} = \frac{V_{C}}{V_{R}}$

$\begin{aligned} V_{C} & = V_{R} X_{C} & = R Z & = \sqrt{(X_{C}^{2} + R^{2})} Z & = R \sqrt{2} \end{aligned}$

Impedance,

[CBSE Marking Scheme 2017]

[AI $Q$ . 2. In a series $L C R$ circuit, obtain the conditions under which (i) the impedance of the circuit is minimum, and (ii) wattless current flows in the circuit.

U] [Foreign 2014]

Ans. (i) The impedance of a series $L C R$ circuit is given by

$Z = \sqrt{R^{2} + {(X_{L} - X_{C})}^{2}}$

$1 / 2$

or For $Z$ to be minimum, $X_{L} = X_{C} ($ or $ω = \frac{1}{\sqrt{L C}}) 1 / 2$

(ii) For wattless current to flow, circuit should not have any ohmic resistance, i.e. $R = 0$ .

Alternatively, Power $= V_{r m s} I_{r m s} \cos ϕ$

for

$ϕ = 90^{\circ} = \frac{π}{2}$

$Power = 0$

$∴$ Wattless current flows when the impedance of the circuit is purely inductive/capacitive or the combination of the two.

[CBSE Marking Scheme 2014]

Alternating Currents

alternating-currents Question 15

Short Answer Type Questions-1

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Alternating Currents

alternating-currents Question 15

Short Answer Type Questions-1

Table of Contents

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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