A circular coil of radius R has a resistance of 40 Ω. Figure shows two points P and Q on the circumference separated by a distance (π R)/(2) which are connected to a 16 V battery with internal resistance of 0.5 Ω. What is the value of current I flowing through the circuit? (a) 3A (b) 2A (c) 1A (d) 0.5A

Answer: (b). Resistance is proportional to arc length. From the figure the two arcs between P and Q are 30 Ω and 10 Ω. They are in parallel: RPQ = (30 × 10)/(30 + 10) = 7.5 Ω Total resistance = 7.5 + 0.5 = 8 Ω I = 16/8 = 2 A. So the answer is (b) 2 A.

A circular coil of radius R has a resistance of 40 Ω. Figure shows… | MHT CET 2020 (16 Oct, Shift 2)

Q60MHT CET 2020 · 16 OCT · SHIFT 2Difficult

Combination of Resistors

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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Answer: (b)

Resistance is proportional to arc length. From the figure the two arcs between $P$ and $Q$ are $30\ \Omega$ and $10\ \Omega$ .
They are in parallel: $R_{PQ} = \frac{30 \times 10}{30 + 10} = 7.5\ \Omega$
Total resistance $= 7.5 + 0.5 = 8\ \Omega$
$I = \frac{16}{8} = 2\text{ A}$ . So the answer is (b) 2 A.

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