Capacitive Circuitsalternating Currents Topic

JEE Advanced

Capacitor

Capacitive reactance: $X_{C} = \frac{1}{2 π f C}$
Current flowing: $I = \frac{V}{X_{C}}$

$X_{C} = \frac{1}{2 π \times 50 Hz \times 100 \times 10^{- 6} F} = 318.31 Ω$

$I = \frac{200 V}{318.31 Ω} = 0.628 A$

AC Circuit with Inductor and Capacitor:

Impedance: $Z = \sqrt{R^{2} + (X_{L} - X_{C})^{2}}$
Current flowing: $I = \frac{V}{Z}$

$X_{L} = 2 π f L = 2 π \times 50 Hz \times 0.1 H = 31.42 Ω$

$Z = \sqrt{10^{2} + (31.42 - 318.31)^{2}} = 300.85 Ω$

$I = \frac{200 V}{300.85 Ω} = 0.665 A$

Step-up Transformer:

Voltage across secondary: $V_{s} = \frac{N_{s}}{N_{p}} V_{p}$

$V_{s} = \frac{200 turns}{100 turns} \times 100 V = 200 V$

CBSE Board Exams

Capacitor

Capacitive reactance: $X_{C} = \frac{1}{2 π f C}$
Current flowing: $I = \frac{V}{X_{C}}$ $X_{C} = \frac{1}{2 π \times 50 Hz \times 100 \times 10^{- 6} F} = 318.31 Ω$

$I = \frac{200 V}{318.31 Ω} = 0.628 A$

AC Circuit with Inductor and Capacitor

Impedance: $Z = \sqrt{R^{2} + (X_{L} - X_{C})^{2}}$
Current flowing: $I = \frac{V}{Z}$

$X_{L} = 2 π f L = 2 π \times 50 Hz \times 0.1 H = 31.42 Ω$

$Z = \sqrt{10^{2} + (31.42 - 318.31)^{2}} = 300.85 Ω$

$I = \frac{200 V}{300.85 Ω} = 0.665 A$

Step-up Transformer:

Voltage across secondary: $V_{s} = \frac{N_{s}}{N_{p}} V_{p}$

$V_{s} = \frac{200 turns}{100 turns} \times 100 V = 200 V$

AC Generator:

Peak voltage: $V_{p e a k} = V_{r m s} \sqrt{2}$ $V_{p e a k} = 220 V \times \sqrt{2} = 311 V$
Peak current: $I_{p e a k} = \frac{V_{p e a k}}{R}$ $I_{p e a k} = \frac{311 V}{100 Ω} = 3.11 A$

Inductor with AC Source:

$I_{r m s} = \frac{V_{r m s}}{Z}, w h e r e Z = \sqrt{R^{2} + X_{L}^{2}}$

$X_{L} = 2 π f L = 2 π (60 Hz) (0.1 H) = 37.7 Ω$

$Z = \sqrt{10^{2} + {37.7}^{2}} = 38.6 Ω$

Current amplitude: $I_{r m s} = \frac{120 V}{38.6 Ω} = 3.11 A$

Capacitor with AC Source:

With $X_{C} = \frac{1}{2 π f C} = 26.52 Ω$

Current amplitude: $I = V_{r m s} \frac{1}{X_{C}} = \frac{120 V}{26.52 Ω} = 4.52 A$

Capacitive Circuitsalternating Currents Topic

JEE Advanced

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Capacitive Circuitsalternating Currents Topic

JEE Advanced

CBSE Board Exams

Table of Contents

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Mentorship

NCERT Exercise Video Solution

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