Question

Resistances of \( 10\ \Omega \) and \( 15\ \Omega \) are connected in parallel. The combination is connected with a battery of \( V \) volt. Choose the correct statement.

• A. Value of current in the \( 10\ \Omega \) resistance will be smaller than the current flowing in the \( 15\ \Omega \) resistance.
• B. Same current will flow in both the resistances.
• C. Potential drop in both the resistances will be different.
• D. Potential drop in both the resistances will be same.

Hint:

Elements in parallel share the same two terminals, so the voltage across each is identical; use \( I = V/R \) to compare currents.

Answer 1

The Correct Option is D

Step 1: Property of a parallel combination.
When two resistances are connected in parallel, both are joined between the same two nodes. Therefore the same potential difference appears across each of them, equal to the battery voltage \( V \).

Step 2: Check the potential drop.
Since both resistors share the same two terminals, the potential drop across the \( 10\ \Omega \) resistor equals the potential drop across the \( 15\ \Omega \) resistor, both \(= V\). This makes option (iv) correct and option (iii) wrong.

Step 3: Check the currents.
By Ohm's law \( I = V/R \). So \( I_{10} = V/10 \) and \( I_{15} = V/15 \). Since \( 10 < 15 \), the current in the \( 10\ \Omega \) resistor is larger, not smaller, and the two currents are not equal. This rules out options (i) and (ii).

Step 4: Conclusion.
The potential drop across both resistances is the same.

\[\boxed{V_{10\Omega} = V_{15\Omega} = V}\]