The resistors of values 3`Omega,6 Omega` and `15Omega` are connected in parallel. What will be equivalent resistance in the circuit?

Options

A. `0.8`
B. `1.4`
C. `2.1`
D. `1.7`

Answer

To find the equivalent resistance of resistors connected in parallel, we can follow these steps:

### Step 1: Identify the resistors
We have three resistors with the following values:
- \( R_1 = 3 \, \Omega \)
- \( R_2 = 6 \, \Omega \)
- \( R_3 = 15 \, \Omega \)

### Step 2: Use the formula for equivalent resistance in parallel
The formula for the equivalent resistance \( R_T \) of resistors in parallel is given by:
\[ \frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} \]

### Step 3: Substitute the values into the formula
Substituting the values of the resistors into the formula:
\[ \frac{1}{R_T} = \frac{1}{3} + \frac{1}{6} + \frac{1}{15} \]

### Step 4: Find a common denominator
The least common multiple (LCM) of the denominators (3, 6, and 15) is 30. We can rewrite each term with a denominator of 30:
\[ \frac{1}{3} = \frac{10}{30}, \quad \frac{1}{6} = \frac{5}{30}, \quad \frac{1}{15} = \frac{2}{30} \]

### Step 5: Add the fractions
Now we can add the fractions:
\[ \frac{1}{R_T} = \frac{10}{30} + \frac{5}{30} + \frac{2}{30} = \frac{17}{30} \]

### Step 6: Take the reciprocal to find \( R_T \)
To find \( R_T \), we take the reciprocal of \( \frac{17}{30} \):
\[ R_T = \frac{30}{17} \]

### Step 7: Calculate the numerical value
Now, we can calculate \( R_T \):
\[ R_T \approx 1.76 \, \Omega \]

### Final Answer
The equivalent resistance \( R_T \) of the circuit is approximately \( 1.76 \, \Omega \).

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