Two conductors A and B resistance `5 omega and 10 omega` respectively are first joined in parallel and then in series. In each case the voltage applied is 20 V.
Equivalant resistance in parallel combination is:

Options

A. `15 omega`
B. `3.33 omega`
C. `0.3 omega`
D. None of the above

Explanation

To find the equivalent resistance of two conductors A and B with resistances of 5 ohms and 10 ohms respectively when they are connected in parallel, we can follow these steps:

### Step 1: Understand the formula for parallel resistance
When resistors are connected in parallel, the formula for the equivalent resistance \( R_{eq} \) is given by:
\[ \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} \]
where \( R_1 \) and \( R_2 \) are the resistances of the individual resistors.

### Step 2: Identify the values of resistances
In this case, we have:
- \( R_1 = 5 \, \Omega \)
- \( R_2 = 10 \, \Omega \)

### Step 3: Substitute the values into the formula
Substituting the values into the formula, we get:
\[ \frac{1}{R_{eq}} = \frac{1}{5} + \frac{1}{10} \]

### Step 4: Calculate the fractions
To add the fractions, we need a common denominator. The least common multiple of 5 and 10 is 10:
\[ \frac{1}{5} = \frac{2}{10} \]
So, we can rewrite the equation as:
\[ \frac{1}{R_{eq}} = \frac{2}{10} + \frac{1}{10} = \frac{3}{10} \]

### Step 5: Take the reciprocal to find \( R_{eq} \)
Now, we take the reciprocal to find the equivalent resistance:
\[ R_{eq} = \frac{10}{3} \, \Omega \approx 3.33 \, \Omega \]

### Final Answer
The equivalent resistance when conductors A and B are connected in parallel is approximately \( 3.33 \, \Omega \).

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