A student is conducting an experiment to determine the resistivity (ρ) of a given wire using a meter bridge. The student sets up the meter bridge experiment as shown below:
The following information is provided:
Known resistance (R1) = 150.0 ohms
Length of wire on one side (l1) = 60.0 cm
Length of wire on the other side (l2) = 120.0 cm
Balance point length (l) = 90.0 cm
Battery voltage (V ) = 5.0 volts
Current through the circuit (I) = 0.3 amperes
Given the formula for the resistivity of a wire:, where A is the cross-sectional area of the wire, calculate the resistivity (ρ) of the given wire.
9.5736 ohm · cm
170 ohm · cm
200 ohm · cm
20 ohm · cm
Using Ohm’s law, we can find the resistance of the wire (R) using the equation
Now, we can substitute the given values into the formula for resistivity (ρ) to solve for it:
Plugging in the known values:
To isolate A, we can rearrange the equation:
Substituting the given values:
Now, we can substitute the calculated value of R back into the equation for A:
Solving for A:
Finally, we can solve for ρ:
Substituting the calculated value of A:
Hence, the resistivity (ρ) of the given wire is approximately 9.5736 ohm · cm. Therefore, the correct answer is A.
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