RC Circuit Phase 90° Condition

 

❓ Question

Given:

R = 100 kΩ
C = 100 pF

Phase difference between:

$$V_{in} \quad \text{and} \quad (V_B - V_A)$$

is 90°.

Input signal frequency:

$$\omega = 10^x \text{ rad/s}$$

Find x.

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🖼 Question Image

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✍️ Short Concept

In an RC circuit:

Capacitive reactance:

$$X_C = \frac{1}{\omega C}$$

90° phase condition usually occurs when:

$$X_C = R$$

👉 That means:

$$\omega = \frac{1}{RC}$$

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🔷 Step 1 — Write Key Relation 💯

For 90° phase condition:

$$\boxed{\omega = \frac{1}{RC}}$$

This is the MOST IMPORTANT step.

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🔷 Step 2 — Convert Values

R = 100 kΩ

$$= 10^5 \, \Omega$$

C = 100 pF

$$= 10^{-10} \, F$$

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🔷 Step 3 — Calculate RC

$$RC = 10^5 \times 10^{-10}$$
$$RC = 10^{-5}$$

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🔷 Step 4 — Find Angular Frequency

$$\omega = \frac{1}{RC}$$
$$= \frac{1}{10^{-5}}$$
$$= 10^5 \text{ rad/s}$$

So,

$$x = 5$$

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✅ Final Answer

$$\boxed{x = 5}$$

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⭐ Golden JEE Insight

Whenever RC circuit + 90° phase given:

Immediately think:

$$X_C = R$$
$$\omega = \frac{1}{RC}$$

⚡ Unit conversion mistake = direct marks loss.