Question

The mutual inductance between a primary and secondary circuit is 0.4 H and the resistance in these circuits are 20 \(\Omega\) and 4 \(\Omega\) respectively. To produce a current of 0.5 A in the secondary, current in the primary must be changed at the rate of

• A. 0.2 A/s
• B. 0.4 A/s
• C. 4 A/s
• D. 5 A/s

Hint:

Find the secondary emf from Ohm's law and equate it with \(M\,dI_p/dt\).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
The emf induced in the secondary is \(\varepsilon_s=M\dfrac{dI_p}{dt}\).

Step 2: Secondary emf
\(\varepsilon_s=I_sR_s=0.5\times4=2\ \text{V}\).

Step 3: Calculation
\(\dfrac{dI_p}{dt}=\dfrac{2}{0.4}=5\ \text{A/s}\).

Final Answer:
The primary current must change at 5 A/s. \[ \boxed{\text{(D) }5\text{ A/s}} \]