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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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In a potentiometer circuit, there is a cell of resistance 5 ohms and e...
To understand why the correct answer is option 'B', let's break down the given information and analyze the potentiometer circuit.
Given:
Resistance of the cell (R1) = 5 ohms
EMF of the cell (E1) = 2 V
Resistance of the wire (R2) = 15 ohms
Length of the wire (L) = 1000 cm
The potentiometer circuit consists of a uniform wire connected in parallel with a cell. The wire is usually made of a material with high resistivity, such as nichrome or constantan.
Potential Gradient:
The potential gradient represents the change in potential per unit length along the wire. It is denoted by (dV/dx).
Formula:
Potential gradient (dV/dx) = EMF (E1) / Total length (L)
Explanation:
1. The potential gradient in the wire is the same as the potential gradient across the cell.
2. The total length of the circuit is the sum of the wire length and the internal resistance length of the cell.
Total length (L) = Wire length + Internal resistance length
Total length (L) = 1000 cm + Internal resistance length
Since the internal resistance of the cell is negligible, we can consider the total length to be equal to the wire length.
Total length (L) = 1000 cm
3. Using the formula for potential gradient, we have:
Potential gradient (dV/dx) = EMF (E1) / Total length (L)
Potential gradient (dV/dx) = 2 V / 1000 cm
Since 1 cm = 0.01 m, we can convert the length to meters:
Potential gradient (dV/dx) = 2 V / (1000 cm * 0.01 m/cm)
Potential gradient (dV/dx) = 2 V / 10 m
Potential gradient (dV/dx) = 0.2 V/m
4. However, the options are given in terms of V/cm. To convert the potential gradient to V/cm, we divide it by 100:
Potential gradient (dV/dx) = 0.2 V/m / 100
Potential gradient (dV/dx) = 0.002 V/cm
5. Simplifying the expression, we have:
Potential gradient (dV/dx) = 3/2000 V/cm
Therefore, the correct answer is option 'B' (3/2000 V/cm).
Given:
Resistance of the cell (R1) = 5 ohms
EMF of the cell (E1) = 2 V
Resistance of the wire (R2) = 15 ohms
Length of the wire (L) = 1000 cm
The potentiometer circuit consists of a uniform wire connected in parallel with a cell. The wire is usually made of a material with high resistivity, such as nichrome or constantan.
Potential Gradient:
The potential gradient represents the change in potential per unit length along the wire. It is denoted by (dV/dx).
Formula:
Potential gradient (dV/dx) = EMF (E1) / Total length (L)
Explanation:
1. The potential gradient in the wire is the same as the potential gradient across the cell.
2. The total length of the circuit is the sum of the wire length and the internal resistance length of the cell.
Total length (L) = Wire length + Internal resistance length
Total length (L) = 1000 cm + Internal resistance length
Since the internal resistance of the cell is negligible, we can consider the total length to be equal to the wire length.
Total length (L) = 1000 cm
3. Using the formula for potential gradient, we have:
Potential gradient (dV/dx) = EMF (E1) / Total length (L)
Potential gradient (dV/dx) = 2 V / 1000 cm
Since 1 cm = 0.01 m, we can convert the length to meters:
Potential gradient (dV/dx) = 2 V / (1000 cm * 0.01 m/cm)
Potential gradient (dV/dx) = 2 V / 10 m
Potential gradient (dV/dx) = 0.2 V/m
4. However, the options are given in terms of V/cm. To convert the potential gradient to V/cm, we divide it by 100:
Potential gradient (dV/dx) = 0.2 V/m / 100
Potential gradient (dV/dx) = 0.002 V/cm
5. Simplifying the expression, we have:
Potential gradient (dV/dx) = 3/2000 V/cm
Therefore, the correct answer is option 'B' (3/2000 V/cm).
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Community 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
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