Question

A direct current of \(6A\) is superimposed on an alternating current given by \( I = 10\sin \omega t \) flowing through a wire. The effective value of the resulting current will be:

• A. \(5\sqrt{2}\)
• B. \(5\sqrt{3}\)
• C. \(9.27\)
• D. \(8.37\)

Hint:

For a combination of AC and DC currents: - RMS value is given by \( I_{{rms}} = \sqrt{I_{{dc}}^2 + I_{{ac,rms}}^2} \). - The RMS value of a sinusoidal AC current \( I = I_0\sin\omega t \) is \( I_{{ac,rms}} = \frac{I_0}{\sqrt{2}} \).

Answer 1

The Correct Option is C

Step 1: Understanding Effective Current Calculation The effective (RMS) value of a current consisting of both direct and alternating components is given by: \[ I_{{rms}} = \sqrt{I_{{dc}}^2 + I_{{ac,rms}}^2} \] where: \( I_{{dc}} = 6A \) (Direct current component), \( I_{{ac}} = 10\sin\omega t \) (AC component with peak value \( I_0 = 10A \)), \( I_{{ac,rms}} = \frac{I_0}{\sqrt{2}} = \frac{10}{\sqrt{2}} = 7.07A \). Step 2: Calculating the Effective Current \[ I_{{rms}} = \sqrt{6^2 + 7.07^2} \] \[ = \sqrt{36 + 50} \] \[ = \sqrt{86} \] \[ \approx 9.27A \] Thus, the correct option is: \[ I_{{rms}} \approx 9.27A \]