Three resistors with magnitudes 2,4 and 8 ohm are connected in parallel. The equivalent resistance of the system would be

Options

A. less than 2 ohm
B. more than 2 ohm but less than 4 ohm
C. 4 ohm
D. 14 ohm

Explanation

To find the equivalent resistance of three resistors connected in parallel, we can use the formula for resistors in parallel:

\[ \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} \]

Where \( R_1, R_2, \) and \( R_3 \) are the resistances of the individual resistors.

### Step-by-Step Solution:

1. **Identify the resistances**:
- \( R_1 = 2 \, \Omega \)
- \( R_2 = 4 \, \Omega \)
- \( R_3 = 8 \, \Omega \)

2. **Substitute the values into the formula**:
\[ \frac{1}{R_{eq}} = \frac{1}{2} + \frac{1}{4} + \frac{1}{8} \]

3. **Calculate each term**:
- \( \frac{1}{2} = 0.5 \)
- \( \frac{1}{4} = 0.25 \)
- \( \frac{1}{8} = 0.125 \)

4. **Add the fractions**:
\[ \frac{1}{R_{eq}} = 0.5 + 0.25 + 0.125 = 0.875 \]

5. **Take the reciprocal to find \( R_{eq} \)**:
\[ R_{eq} = \frac{1}{0.875} = \frac{8}{7} \approx 1.14 \, \Omega \]

### Final Answer:
The equivalent resistance \( R_{eq} \) of the system is approximately \( 1.14 \, \Omega \).

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