A circular coil of radius \( R \) has a resistance of 40\( \Omega \). Figure shows two points \( P \) and \( Q \) on the circumference separated by a distance \( \frac{\pi R}{2} \), which are connected to a 16 V battery with internal resistance of 0.5 \( \Omega \). What is the value of current \( I \) flowing through the circuit?
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For circuits with internal resistance, always add the internal resistance to the total resistance of the external components.
Step 1: Resistance of the coil.
The resistance of the coil is \( R_{\text{coil}} = 40 \, \Omega \).
Step 2: Effective resistance of the circuit.
The distance between \( P \) and \( Q \) is \( \frac{\pi R}{2} \), and the total resistance in the loop includes the resistance of the coil and the internal resistance of the battery, which is \( R_{\text{int}} = 0.5 \, \Omega \).
The total resistance in the circuit is:
\[
R_{\text{total}} = 40 + 0.5 = 40.5 \, \Omega
\]
Step 3: Apply Ohm's law.
Using Ohm’s law, the current is:
\[
I = \frac{V}{R_{\text{total}}} = \frac{16}{40.5} \approx 2 \, \text{A}
\]
Step 4: Conclusion.
The current flowing through the circuit is 2 A, so the correct answer is (D).
