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

Options

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

Answer

To solve the problem, we need to find the current flowing through the 3-ohm resistor when a 1.5-volt cell is connected across it. The resistors are arranged in a triangular configuration, with values of 1 ohm, 2 ohms, and 3 ohms.

### Step-by-Step Solution:

1. **Identify the Configuration**:
We have three resistors: R1 = 1 ohm, R2 = 2 ohms, and R3 = 3 ohms. They are connected in a triangular shape.

2. **Connect the Voltage Source**:
A 1.5-volt cell is connected across the 3-ohm resistor (R3). The internal resistance of the cell is negligible.

3. **Determine Equivalent Resistance**:
- The 1-ohm (R1) and 2-ohm (R2) resistors are in series.
- The equivalent resistance of R1 and R2 (let's call it R1,2) is:
\[ R_{1,2} = R1 + R2 = 1 \, \text{ohm} + 2 \, \text{ohm} = 3 \, \text{ohm} \]
- Now, R1,2 (3 ohm) is in parallel with R3 (3 ohm).

4. **Calculate the Equivalent Resistance of the Parallel Combination**:
- The formula for resistors in parallel is:
\[ \frac{1}{R_{eq}} = \frac{1}{R_{1,2}} + \frac{1}{R_{3}} \]
- Substituting the values:
\[ \frac{1}{R_{eq}} = \frac{1}{3} + \frac{1}{3} = \frac{2}{3} \]
- Therefore, the equivalent resistance (R_eq) is:
\[ R_{eq} = \frac{3}{2} \, \text{ohm} = 1.5 \, \text{ohm} \]

5. **Calculate the Total Current Using Ohm's Law**:
- The total current (I) from the voltage source can be calculated using Ohm's Law:
\[ I = \frac{V}{R_{eq}} = \frac{1.5 \, \text{V}}{1.5 \, \text{ohm}} = 1 \, \text{A} \]

6. **Determine the Current Through the 3-ohm Resistor**:
- Since the current splits between the two branches (R1,2 and R3), we use the current division rule.
- The current through R3 (I3) can be found using:
\[ I3 = \frac{R_{1,2}}{R_{1,2} + R_{3}} \times I \]
- Substituting the values:
\[ I3 = \frac{3}{3 + 3} \times 1 = \frac{3}{6} = 0.5 \, \text{A} \]

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