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: Draw the nodes.
In a parallel network the two resistors have their left ends tied together and their right ends tied together, and these two junction points are the battery terminals. Voltage is a property of the junction pair, so whatever appears across one branch appears across the other.

Step 2: Fix the common voltage.
That common voltage is simply the battery e.m.f. \(V\). Hence \(V_{10} = V_{15} = V\); the drops are identical, confirming statement (iv) and killing statement (iii).

Step 3: Compare branch currents with Ohm's law.
Current in a branch is \(I = V/R\). The smaller resistance carries the bigger current, so \(I_{10} = V/10\) exceeds \(I_{15} = V/15\). Thus the \(10\,\Omega\) current is greater (statement (i) claims the opposite, so it is false), and the currents are unequal (statement (ii) is false).

Step 4: Select.
Only the equal-potential-drop statement survives.

\[\boxed{\text{Same potential drop across both}}\]