SATHEE: Electromagnetic Induction and Alternating Current 4 Question 5

Electromagnetic Induction and Alternating Current 4 Question 5

5. A series $A C$ circuit containing an inductor $(20 m H)$ , a capacitor $(120 μ F)$ and a resistor $(60 Ω)$ is driven by an $A C$ source of $24 V / 50 H z$ . The energy dissipated in the circuit in $60 s$ is

(Main 2019, 9 Jan II)

(a) $3.39 \times 10^{3} J$

(b) $5.65 \times 10^{2} J$

(d) $5.17 \times 10^{2} J$

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Answer:

Correct Answer: 5. (d)

Solution:

The given series $R - L - C$ circuit is shown in the figure below.

Here,

$V_{R} =$ potential across resistance $(R)$

$V_{L} =$ potential across inductor $(L)$ and

$V_{C} =$ potential across capacitor $(C)$

Impedance of this series circuit is

$\begin{aligned} Z & = \sqrt{R^{2} + {(X_{L} - X_{C})}^{2}} \\ ∵ X_{L} & = ω L = (2 π f) (L) \\ = 2 π \times 50 \times 20 \times 10^{- 3} Ω \\ X_{L} & = 6.28 Ω \\ X_{C} & = \frac{1}{ω C} = \frac{1}{2 π f C} \\ = \frac{1}{2 π \times 50 \times 120 \times 10^{- 6}} = \frac{250}{3 π} Ω \\ and X_{L} - X_{C} & = 6.28 - \frac{250}{3 π} = - 20.23 Ω \end{aligned}$

RMS value of current in circuit is

$\begin{aligned} I_{r m s} = \frac{V_{r m s}}{Z} = \frac{24}{\sqrt{R^{2} + {(X_{L} - X_{C})}^{2}}} \\ I_{r m s} = \frac{24}{\sqrt{60^{2} + (- 20.23)^{2}}} = \frac{24}{63.18} \\ I_{r m s} = 0.379 A \end{aligned}$

Therefore, energy dissipated is

$\begin{aligned} = I_{r m s}^{2} \times R \times t \\ E & = (0.379)^{2} \times 60 \times 60 \\ = 517.10 = 5.17 \times 10^{2} J \end{aligned}$

Electromagnetic Induction and Alternating Current 4 Question 5

5. A series $A C$ circuit containing an inductor $(20 m H)$ , a capacitor $(120 μ F)$ and a resistor $(60 Ω)$ is driven by an $A C$ source of $24 V / 50 H z$ . The energy dissipated in the circuit in $60 s$ is

Answer:

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Electromagnetic Induction and Alternating Current 4 Question 5

5. A series AC circuit containing an inductor (20mH), a capacitor (120μF) and a resistor (60Ω) is driven by an AC source of 24V/50Hz. The energy dissipated in the circuit in 60s is

Answer:

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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5. A series $A C$ circuit containing an inductor $(20 m H)$ , a capacitor $(120 μ F)$ and a resistor $(60 Ω)$ is driven by an $A C$ source of $24 V / 50 H z$ . The energy dissipated in the circuit in $60 s$ is