Question

A series RLC circuit has \(L=0.5\,\text{H}\), \(C=0.02\,\text{F}\). For critical damping, the required resistance \(R\) is

• A. \(5\,\Omega\)
• B. \(10\,\Omega\)
• C. \(20\,\Omega\)
• D. \(40\,\Omega\)

Hint:

For a series RLC circuit, \[ \boxed{ R_c=2\sqrt{\frac{L}{C}} } \] where \(R_c\) is the critical damping resistance.

Answer 1

The Correct Option is B

Step 1: Use the condition for critical damping. For a series RLC circuit, \[ R_c=2\sqrt{\frac{L}{C}}. \] Given, \[ L=0.5\,\text{H},\qquad C=0.02\,\text{F}. \]

Step 2: Calculate the critical resistance. \[ R_c = 2\sqrt{\frac{0.5}{0.02}} = 2\sqrt{25} = 2\times5 = 10\,\Omega. \] Hence, \[ \boxed{10\,\Omega} \] Therefore, \[ \boxed{(B)} \] is the correct answer.