NEET#

1. Capacitor

• Capacitive reactance: $$X_C=\frac{1}{2\pi fC}$$
• Current flowing: $$I=\frac{V}{X_C}$$

$$X_C= \frac{1}{2\pi \times 50 \text{ Hz} \times 100\times 10^{-6} \text{ F}}=318.31\Omega$$

$$I=\frac{200\text{ V}}{318.31\Omega}=\boxed{0.628 \text{ A}}$$

2. AC Circuit with Inductor and Capacitor:

• Impedance: $$Z=\sqrt{R^2+(X_L-X_C)^2}$$
• Current flowing: $$I=\frac{V}{Z}$$

$$X_L=2\pi f L=2\pi \times 50\text{ Hz}\times 0.1\text{ H}=31.42 \Omega$$

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

$$I=\frac{200\text{ V}}{300.85\Omega}=\boxed{0.665 \text{ A}}$$

3. Step-up Transformer:

• Voltage across secondary: $$V_s=\frac{N_s}{N_p}V_p$$

$$V_s=\frac{200\ \text{ turns}}{100\text{ turns}}\times100\text{ V}=\boxed{200\text{ V}}$$

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CBSE Board Exams#

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1. Capacitor

• Capacitive reactance: $$X_C=\frac{1}{2\pi fC}$$

• Current flowing: $$I=\frac{V}{X_C}$$ $$X_C=\frac{1}{2\pi\times 50 \text{ Hz}\times 100\times10^{-6}\text{ F}}=\boxed{318.31 \Omega}$$

$$I=\frac{200\text{ V}}{318.31\Omega}=\boxed{0.628\text{ A}}$$

2. AC Circuit with Inductor and Capacitor

• Impedance: $$Z=\sqrt{R^2+(X_L-X_C)^2}$$

• Current flowing: $$I=\frac{V}{Z}$$

$$X_L=2\pi fL=2\pi\times50\text{ Hz}\times0.1\text{ H}=31.42\Omega$$

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

$$I=\frac{200\text{ V}}{300.85\Omega}=\boxed{0.665\text{ A}}$$

3. Step-up Transformer:

• Voltage across secondary: $$V_s=\frac{N_s}{N_p}V_p$$

$$V_s=\frac{200\text{ turns}}{100\text{ turns}}\times100\text{ V}=\boxed{200\text{ V}}$$

4. AC Generator:

• Peak voltage: $$V_{peak}=V_{rms}\sqrt{2}$$ $$V_{peak}=220 \text{ V}\times \sqrt{2}=\boxed{311\text{ V}}$$

• Peak current: $$I_{peak}=\frac{V_{peak}}{R}$$ $$I_{peak}=\frac{311 \text{ V}}{100 \Omega}=\boxed{3.11\text{ A}}$$

5. Inductor with AC Source:

• $$I_{rms}=\frac{V_{rms}}{Z}, where Z=\sqrt{R^2+X_L^2}$$

$$X_L=2\pi fL=2\pi (60\text{ Hz})(0.1\text{ H})=37.7\Omega$$

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

• Current amplitude: $$I_{rms}=\frac{120\text{ V}}{38.6 \Omega}=\boxed{3.11 \text{ A}}$$

6. Capacitor with AC Source:

With $$X_C=\frac{1}{2\pi fC}=26.52 \Omega$$

• Current amplitude: $$I=V_{rms} \frac{1}{X_C}=\frac{120\text{ V}}{26.52\Omega}=\boxed{4.52 \text{ A}}$$