To determine the resistance (R) of a wire, a circuit is designed below. The V-I characteristic curve for this circuit is plotted for the voltmeter and the ammeter readings as shown in figure. The value of R is _________ Ω.

Solution

Physics sir · 3 steps

The graph gives the resistance of R and the 10 kΩ together, not R alone. Peel off the 10 kΩ.

1. Read the circuit. The voltmeter sits across both R and the 10 kΩ resistor, which are in parallel. The milliammeter reads the total current through that parallel pair.
2. Read the graph. The line passes through the origin, and at V = 4 V the current is I = 2 mA. So V/I = 4/(2 × 10⁻³) = 2000 Ω, which is the equivalent resistance R_(eq) of the pair.

   1/R_(eq) = 1/R + 1/10000 ⇒ 1/R = 1/2000 - 1/10000 = 4/10000

3. So. R = 10000/4 = 2500 Ω, so the answer is 2500.

The common slip: 2000. Taking V/I from the graph as R itself gives 2000. That value is R in parallel with the 10 kΩ resistor.

The idea to keep. Before reading a resistance off a V-I graph, check what the meters are actually across. If another resistor shares those terminals, the slope gives the combination.

Answer from the NTA final answer key. Solution by PrepWiser.