Three resistors of `1 Omega, 2 Omega and 3 Omega` are connected in parallel. The combined resistance of 3 resistors should be

Options

A. greater than `3 Omega`
B. lesser than `1 Omega`
C. equal to `2 Omega`
D. between `1 Omega and 3 Omega`

Answer

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

### Step 1: Understand the formula for parallel resistors
When resistors are connected in parallel, the formula for the equivalent resistance \( R_{eq} \) is given by:
\[ \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} \]

### Step 2: Identify the values of the resistors
In this case, we have three resistors:
- \( R_1 = 1 \, \Omega \)
- \( R_2 = 2 \, \Omega \)
- \( R_3 = 3 \, \Omega \)

### Step 3: Substitute the values into the formula
Now we substitute the values of the resistors into the formula:
\[ \frac{1}{R_{eq}} = \frac{1}{1} + \frac{1}{2} + \frac{1}{3} \]

### Step 4: Calculate each term
Calculating each term gives us:
\[ \frac{1}{1} = 1 \]
\[ \frac{1}{2} = 0.5 \]
\[ \frac{1}{3} \approx 0.333 \]

### Step 5: Add the fractions
Now we add these values together:
\[ \frac{1}{R_{eq}} = 1 + 0.5 + 0.333 = 1.833 \]

### Step 6: Find the equivalent resistance
To find \( R_{eq} \), we take the reciprocal of the sum:
\[ R_{eq} = \frac{1}{1.833} \approx 0.545 \, \Omega \]

### Step 7: Round the answer
Rounding to two decimal places, we find:
\[ R_{eq} \approx 0.54 \, \Omega \]

### Final Answer
The combined resistance of the three resistors connected in parallel is approximately \( 0.54 \, \Omega \).

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