Question

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 the figure. The value of \( R \) is \( \dots \dots \dots \Omega \).

Answer 1

Correct Answer: 2500

Ohm's Law, \( V = IR \), defines the relationship between voltage (\( V \)), current (\( I \)), and resistance (\( R \)). To find the wire's resistance \( R \), we consider a circuit where a 10 kΩ resistor is connected in parallel with \( R \). The total resistance (\( R_t \)) for parallel resistors is calculated using \( \frac{1}{R_t} = \frac{1}{R} + \frac{1}{10000} \).
From the provided graph, at a voltage of 8 V, the current is \( I = 4 \) mA, which is equal to \( 0.004 \) A.
Applying Ohm's law to determine the total resistance at 8 V yields \( R_t = \frac{8}{0.004} = 2000 \, \Omega \).

Substituting \( R_t = 2000 \, \Omega \) into the parallel resistance formula gives:
\( \frac{1}{2000} = \frac{1}{R} + \frac{1}{10000} \).
Solving for \( R \), we get:
\( \frac{1}{R} = \frac{1}{2000} - \frac{1}{10000} = \frac{5}{10000} - \frac{1}{10000} = \frac{4}{10000} \).
Therefore, \(R = \frac{10000}{4} = 2500 \ \Omega .\)

The calculated resistance for \( R \) is \( 2500 \, \Omega \), which falls within the specified range of (2500, 2500).