If you are provided three resistance `2 Omega, 3 Omega` and `6 Omega`. How will you connect them so as to obtain the equivalent resistance of `4 Omega`

Options

A.
B.
C.
D. none

Explanation

To solve the problem of obtaining an equivalent resistance of 4 ohms using the resistances of 2 ohms, 3 ohms, and 6 ohms, we can analyze the possible configurations of these resistors.

### Step-by-Step Solution:

1. **Understanding Series and Parallel Connections**:
- In a series connection, the equivalent resistance (R_eq) is the sum of the individual resistances:
\[ R_{eq} = R_1 + R_2 + R_3 + \ldots \]
- In a parallel connection, the equivalent resistance is given by:
\[ \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \ldots \]

2. **Testing Different Configurations**:
- We will check various combinations of the given resistances to find one that results in an equivalent resistance of 4 ohms.

3. **Option A**: Connect 3 ohms and 6 ohms in series, then in parallel with 2 ohms.
- Series combination:
\[ R_{series} = 3 + 6 = 9 \, \Omega \]
- Now, calculate the equivalent resistance with 2 ohms in parallel:
\[ \frac{1}{R_{eq}} = \frac{1}{9} + \frac{1}{2} = \frac{2 + 9}{18} = \frac{11}{18} \]
\[ R_{eq} = \frac{18}{11} \approx 1.64 \, \Omega \quad \text{(not equal to 4 ohms)} \]

4. **Option B**: Connect 3 ohms and 2 ohms in series, then in parallel with 6 ohms.
- Series combination:
\[ R_{series} = 3 + 2 = 5 \, \Omega \]
- Now, calculate the equivalent resistance with 6 ohms in parallel:
\[ \frac{1}{R_{eq}} = \frac{1}{5} + \frac{1}{6} = \frac{6 + 5}{30} = \frac{11}{30} \]
\[ R_{eq} = \frac{30}{11} \approx 2.73 \, \Omega \quad \text{(not equal to 4 ohms)} \]

5. **Option C**: Connect 3 ohms and 6 ohms in parallel, then add 2 ohms in series.
- Parallel combination:
\[ \frac{1}{R_{parallel}} = \frac{1}{3} + \frac{1}{6} = \frac{2 + 1}{6} = \frac{3}{6} = \frac{1}{2} \]
\[ R_{parallel} = 2 \, \Omega \]
- Now, add the 2 ohms in series:
\[ R_{eq} = 2 + 2 = 4 \, \Omega \quad \text{(this is equal to 4 ohms)} \]

6. **Conclusion**:
- The configuration that gives an equivalent resistance of 4 ohms is to connect the 3-ohm and 6-ohm resistors in parallel and then connect the resulting 2-ohm resistance in series with the 2-ohm resistor.

### Final Answer:
The equivalent resistance of 4 ohms can be obtained by connecting the 3-ohm and 6-ohm resistors in parallel, and then connecting the resulting 2-ohm resistance in series with the 2-ohm resistor.