When a know standard resistor of 2.0Ω is connected to the 0.Ocm end of a meter bridge,the balance point is found to be at 55.0cm.what is the value of the unknown resistor?
A.1.10Ω
B.1.64Ω
C.2.44Ω
D.27.50Ω?
To find the value of the unknown resistor using a meter bridge, we can use the principle of Wheatstone's Bridge.
In this case, a known standard resistor of 2.0Ω is connected to one end of the meter bridge (0.0cm), and the balance point is found to be at 55.0cm.
The principle of the meter bridge states that when the balance point is reached, the ratio of the resistances on one side of the bridge is equal to the ratio of the resistances on the other side.
In this case, the ratio of the resistance on one side of the bridge (from the 0.0cm end to the balance point) can be calculated as:
Ratio = distance from the unknown resistor to the balance point / distance from the known resistor to the balance point
Ratio = (55.0cm - 0.0cm) / (100.0cm - 55.0cm) = 55.0cm / 45.0cm = 1.22
Since we know the resistance of the known resistor is 2.0Ω, we can set up the following equation:
1.22 = unknown resistor / 2.0Ω
Solving for the unknown resistor:
unknown resistor = 1.22 * 2.0Ω ≈ 2.44Ω
Therefore, the value of the unknown resistor is approximately 2.44Ω.
So, the correct answer is option C: 2.44Ω.