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In a potentiometer circuit, there is a cell of resistance 5 ohms and emf 2 V connected to a uniform wire of length 1000 cm and resistance 15 ohms. The potential gradient in the wire is
- a)1/500 V/cm
- b)3/2000 V/cm
- c)3/5000 V/cm
- d)1/1000 V/cm
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
In a potentiometer circuit, there is a cell of resistance 5 ohms and e...
Voltage across the ends of the potentiometer wire:
Where V is emf of the cell, R is the resistance of the wire and r is the internal resistance of cell
L = 1000 cm
Potential gradient (k) = V0/L
Where V is emf of the cell, R is the resistance of the wire and r is the internal resistance of cell
L = 1000 cm
Potential gradient (k) = V0/L
Most Upvoted Answer
In a potentiometer circuit, there is a cell of resistance 5 ohms and e...
Given data:
Resistance of the cell, \(R_1 = 5 \, \Omega\)
EMF of the cell, \(E = 2 \, V\)
Resistance of the wire, \(R_2 = 15 \, \Omega\)
Length of the wire, \(L = 1000 \, cm = 10 \, m\)
Calculating potential gradient:
The total resistance in the circuit can be calculated as:
\[
R_{total} = R_1 + R_2 = 5 \, \Omega + 15 \, \Omega = 20 \, \Omega
\]
The total current in the circuit can be calculated using Ohm's Law:
\[
I = \frac{E}{R_{total}} = \frac{2 \, V}{20 \, \Omega} = 0.1 \, A
\]
The potential gradient in the wire can be calculated using the formula:
\[
V = I \cdot R
\]
where \(V\) is the potential difference across the wire, \(I\) is the current passing through the wire, and \(R\) is the resistance of the wire.
Substitute the values:
\[
V = 0.1 \, A \cdot 15 \, \Omega = 1.5 \, V
\]
The potential gradient can be calculated as:
\[
\text{Potential gradient} = \frac{V}{L} = \frac{1.5 \, V}{10 \, m} = 0.15 \, V/m = 3/2000 \, V/cm
\]
Therefore, option 'B' is the correct answer - 3/2000 V/cm.
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