Resistors of 1, 2, 3 ohm are connected in the form of a triangle. If a `1.5 V` cell of negligible internal resistance is connected across 3 ohm resistor, the current flowing through this resistance will be

Options

A. 0.25 A
B. 0.5 A
C. 1.0 A
D. 1.5 A

Answer

To solve the problem step by step, we need to analyze the circuit formed by the resistors and apply Ohm's law. Here’s how we can do it:

### Step 1: Understand the Circuit Configuration
We have three resistors of 1 ohm, 2 ohm, and 3 ohm connected in a triangular configuration. The 1.5 V cell is connected across the 3 ohm resistor.

### Step 2: Identify the Resistors
Let's label the resistors:
- R1 = 1 ohm
- R2 = 2 ohm
- R3 = 3 ohm

### Step 3: Determine the Equivalent Resistance
Since the resistors are connected in a triangle, we can find the equivalent resistance between points A and C (across the 3 ohm resistor). The resistors R1 and R2 are in series with the 3 ohm resistor.

1. The equivalent resistance \( R_{eq} \) can be calculated using the formula for resistors in series:
\[ R_{eq} = R1 + R2 = 1 \, \text{ohm} + 2 \, \text{ohm} = 3 \, \text{ohm} \]

2. Now, the total resistance in the circuit when the 3 ohm resistor is connected across the voltage source is:
\[ R_{total} = R_{eq} \parallel R3 = \frac{R_{eq} \cdot R3}{R_{eq} + R3} = \frac{3 \cdot 3}{3 + 3} = \frac{9}{6} = 1.5 \, \text{ohm} \]

### Step 4: Apply Ohm's Law to Find Current
Using Ohm's Law, we can find the current flowing through the 3 ohm resistor:
\[ I = \frac{V}{R} = \frac{1.5 \, \text{V}}{1.5 \, \text{ohm}} = 1 \, \text{A} \]

### Step 5: Determine Current Distribution
Since the current splits at the junction, we can find the current through the 3 ohm resistor. The voltage across the 3 ohm resistor is:
\[ V = I \cdot R3 = 1 \, \text{A} \cdot 3 \, \text{ohm} = 3 \, \text{V} \]
However, since we only have a 1.5 V source, the current through the 3 ohm resistor is:
\[ I_{3 \, \text{ohm}} = \frac{1.5 \, \text{V}}{3 \, \text{ohm}} = 0.5 \, \text{A} \]

### Final Answer
The current flowing through the 3 ohm resistor is **0.5 A**.

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