Question

In an AC circuit, the rms value of current is \(5\ \text{A}\). The peak current is:

• A. \(3.54\ \text{A}\)
• B. \(5\ \text{A}\)
• C. \(7.07\ \text{A}\)
• D. \(10\ \text{A}\)

Hint:

For AC current: \[ I_{\text{rms}}=\frac{I_0}{\sqrt2} \] Hence: \[ I_0=\sqrt2\,I_{\text{rms}} \]

Answer 1

The Correct Option is C

For alternating current: \[ I_{\text{rms}}=\frac{I_0}{\sqrt2} \] where:
• \(I_{\text{rms}}\) = rms current
• \(I_0\) = peak current Given: \[ I_{\text{rms}}=5\ \text{A} \]
Step 1: Find peak current \[ I_0=\sqrt2\,I_{\text{rms}} \] Substituting the value: \[ I_0=\sqrt2\times5 \] \[ I_0=1.414\times5 \] \[ I_0=7.07\ \text{A} \] Thus: \[ \boxed{I_0=7.07\ \text{A}} \] Option analysis:
• Option (A): Incorrect
• Option (B): Incorrect
• Option (C): Correct
• Option (D): Incorrect Therefore: \[ \boxed{\text{(C)}} \]