Question

Two resistors of 0·4 Ω and 0·6 Ω are connected in parallel combination. Their equivalent resistance is

• A. 1 Ω
• B. 0·5 Ω
• C. 0·24 Ω
• D. 0·1 Ω

Answer 1

The Correct Option is C

When two resistors are connected in parallel, their equivalent resistance \( R_{\text{eq}} \) can be calculated using the formula:

$$ \frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2} $$

Here, \( R_1 = 0.4 \, \Omega \) and \( R_2 = 0.6 \, \Omega \).

Substituting the values:

$$ \frac{1}{R_{\text{eq}}} = \frac{1}{0.4} + \frac{1}{0.6} $$

Calculating each term gives:

$$ \frac{1}{0.4} = 2.5 $$

$$ \frac{1}{0.6} = 1.6667 $$

Adding these results:

$$ \frac{1}{R_{\text{eq}}} = 2.5 + 1.6667 = 4.1667 $$

Taking the reciprocal to find \( R_{\text{eq}} \):

$$ R_{\text{eq}} = \frac{1}{4.1667} $$

Therefore, the equivalent resistance is:

$$ R_{\text{eq}} \approx 0.24 \, \Omega $$

Thus, the correct answer is \( R_{\text{eq}} = 0.24 \, \Omega \).

Answer 2

Given: Two resistors in parallel, \( R_1 = 0.4\, \Omega \), \( R_2 = 0.6\, \Omega \)

The formula for equivalent resistance \( R \) in a parallel combination is:

\[ \frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} = \frac{1}{0.4} + \frac{1}{0.6} \]

\[ \frac{1}{R} = \frac{5}{2} + \frac{5}{3} = \frac{15 + 10}{6} = \frac{25}{6} \Rightarrow R = \frac{6}{25} = 0.24\, \Omega \]

Final Answer: 0·24 Ω