Question

For a resistor \( R \), the potential across it is given by \( 1.6 \times 10^{-6} \, \text{C} \) of charge and a voltage across it. The electrical potential due to this charge will depend on:

• A. \( \frac{1}{R} \)
• B. \( 1.6 \times 10^7 R \)
• C. \( R \)
• D. \( 1.6 \times 10^7 R^2 \)

Hint:

In circuits, the electrical potential depends on the resistance, as described by the formula \( V = IR \), where \( I \) is the current and \( R \) is the resistance.

Answer 1

The Correct Option is C

Step 1: Electric potential formula.
The potential \( V \) across a resistor is related to the charge \( Q \) and the resistance \( R \) by the formula: \[ V = \frac{Q}{C} \] where \( C \) is the capacitance of the system.
Step 2: Using the charge.
Since the total charge is \( Q = 1.6 \times 10^{-6} \, \text{C} \), the potential across the resistor will be directly proportional to \( R \).
Step 3: Conclusion.
Thus, the potential will depend on the value of \( R \), so the correct answer is (C).