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A potentiometer wire of length 10 m and resistance 20Ω is connected in series with a 25 V battery and an external resistance 30Ω. A cell of emf E in secondary circuit is balanced by 250 cm long potentiometer wire. The value of E (in volts) is x/10. The value of x is __________. (In integers)
Correct answer is '2.5'. Can you explain this answer?
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A potentiometer wire of length 10 m and resistance 20Ω is connec...
Ω is connected to a 6 V battery. The potential gradient along the wire is 0.6 V/m. Find the potential difference between the ends of the wire when a resistance of 12 Ω is connected between a point on the wire 3 m from one end and the other end.
We can start by finding the total resistance of the potentiometer wire. Since the wire has a length of 10 m and a resistance of 20 Ω, the resistance per unit length is:
R = 20 Ω / 10 m = 2 Ω/m
The potential gradient along the wire is given as 0.6 V/m. This means that the potential difference between two points on the wire separated by a distance of 1 m is:
V = 0.6 V/m × 1 m = 0.6 V
To find the potential difference between the ends of the wire, we need to determine the potential difference between the end of the wire and the point where the 12 Ω resistor is connected. Let's call this point P.
We can use the potential divider rule to determine the potential difference between the ends of the wire and point P:
V_P = (R_P / R_T) × V_T
where R_P is the resistance between point P and the end of the wire, R_T is the total resistance of the wire, and V_T is the voltage of the battery (6 V).
To find R_P, we need to add the resistance of the 12 Ω resistor to the resistance of the wire from point P to the end of the wire:
R_P = 12 Ω + 2 Ω/m × (10 m - 3 m) = 20 Ω
Therefore, the potential difference between the ends of the wire and point P is:
V_P = (20 Ω / 20 Ω) × 6 V = 6 V
Finally, the potential difference between the ends of the wire is:
V = V_T - V_P = 6 V - 6 V = 0 V
Therefore, when a resistance of 12 Ω is connected between a point on the wire 3 m from one end and the other end, the potential difference between the ends of the wire is zero. This means that the 12 Ω resistor is balanced and the potential at point P is the same as the potential at the end of the wire.
We can start by finding the total resistance of the potentiometer wire. Since the wire has a length of 10 m and a resistance of 20 Ω, the resistance per unit length is:
R = 20 Ω / 10 m = 2 Ω/m
The potential gradient along the wire is given as 0.6 V/m. This means that the potential difference between two points on the wire separated by a distance of 1 m is:
V = 0.6 V/m × 1 m = 0.6 V
To find the potential difference between the ends of the wire, we need to determine the potential difference between the end of the wire and the point where the 12 Ω resistor is connected. Let's call this point P.
We can use the potential divider rule to determine the potential difference between the ends of the wire and point P:
V_P = (R_P / R_T) × V_T
where R_P is the resistance between point P and the end of the wire, R_T is the total resistance of the wire, and V_T is the voltage of the battery (6 V).
To find R_P, we need to add the resistance of the 12 Ω resistor to the resistance of the wire from point P to the end of the wire:
R_P = 12 Ω + 2 Ω/m × (10 m - 3 m) = 20 Ω
Therefore, the potential difference between the ends of the wire and point P is:
V_P = (20 Ω / 20 Ω) × 6 V = 6 V
Finally, the potential difference between the ends of the wire is:
V = V_T - V_P = 6 V - 6 V = 0 V
Therefore, when a resistance of 12 Ω is connected between a point on the wire 3 m from one end and the other end, the potential difference between the ends of the wire is zero. This means that the 12 Ω resistor is balanced and the potential at point P is the same as the potential at the end of the wire.
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A potentiometer wire of length 10 m and resistance 20Ω is connected in series with a 25 V battery and an external resistance 30Ω. A cell of emf E in secondary circuit is balanced by 250 cm long potentiometer wire. The value of E (in volts) is x/10. The value of x is __________. (In integers)Correct answer is '2.5'. Can you explain this answer?
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