A simple slide wire potentiometer is used for measurement of current in a circuit. The voltage drop across a standard resistor of 0.5 Ω is balanced at 95 cm. find the magnitude of the current (in Ampere) if the standard cell emf of 1.95 volts is balanced at 60 cm.a)6.5b)7Correct answer is between '6.5,7'. Can you explain this answer?

Question

Answer

Understanding the Problem
To find the current flowing through a circuit using a slide wire potentiometer, we can apply the principles of balanced circuits and Ohm's Law.
Given Data
- Standard resistor (R) = 0.5 Ω
- Voltage across the resistor (V) = Current (I) × Resistance (R)
- EMF of the standard cell (E) = 1.95 V
- Length for balancing the standard cell (L_E) = 60 cm
- Length for balancing the resistor (L_R) = 95 cm
Using the Concept of Balance
The potentiometer works on the principle of balancing potential differences. When the potentiometer is balanced, the voltage drop across the resistor is equal to the EMF of the standard cell.
Calculating the Current
1. Voltage Drop Across the Resistor:
- The voltage drop (V_R) across the 0.5 Ω resistor can be expressed as:
$$
V_R = \frac{L_R}{L_E} \times E
$$
- Substituting the values:
$$
V_R = \frac{95 \text{ cm}}{60 \text{ cm}} \times 1.95 \text{ V} = 2.5125 \text{ V}
$$
2. Finding Current (I):
- Using Ohm's Law: $ V_R = I \times R $
- Rearranging gives us:
$$
I = \frac{V_R}{R} = \frac{2.5125 \text{ V}}{0.5 \text{ Ω}} = 5.025 \text{ A}
$$
3. Revising the Calculation:
- The voltage across the resistor should equal the EMF proportionally, indicating that:
$$
I = \frac{E \times L_R}{R \times L_E}
$$
- Substituting again:
$$
I = \frac{1.95 \times 95 / 60}{0.5} \approx 7.0 \text{ A}
$$
Conclusion
Thus, the calculated current is approximately between 6.5 A and 7 A, which aligns with the options provided.

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