To solve this problem, we first need to determine the total resistance of the potentiometer wire and the resistance box when a potential difference of 100 mV is balanced across the entire length of the wire.
Calculating Total Resistance
The potentiometer wire is 10 meters long with a resistance of 10 Ω per meter. Therefore, the total resistance of the wire is:
- Total Resistance of Wire = Length × Resistance per Meter
- Total Resistance of Wire = 10 m × 10 Ω/m = 100 Ω
Understanding the Circuit
The total voltage supplied by the battery is 2 volts. When the potential difference of 100 mV (or 0.1 V) is balanced across the potentiometer wire, we can use Ohm's Law (V = IR) to find the current flowing through the circuit.
Finding the Current
The current flowing through the potentiometer wire can be calculated as follows:
- Voltage across the wire = 0.1 V
- Using Ohm's Law: I = V/R
- Current (I) = 0.1 V / 100 Ω = 0.001 A (or 1 mA)
Calculating Total Resistance in the Circuit
Now, we can find the total resistance in the circuit using the total voltage and the current:
- Total Voltage = 2 V
- Total Resistance (R_total) = Total Voltage / Current
- R_total = 2 V / 0.001 A = 2000 Ω
Finding Resistance in the Resistance Box
The total resistance in the circuit is the sum of the resistance of the potentiometer wire and the resistance in the resistance box (R_box):
- R_total = R_wire + R_box
- 2000 Ω = 100 Ω + R_box
- R_box = 2000 Ω - 100 Ω = 1900 Ω
Therefore, the resistance introduced in the resistance box is 1900 Ω, which corresponds to option (a).
