Four unequal resistors are connected in parallel. Which one of the following statements is correct?

Options

A. The total resistance is less than the smallest resistor
B. The total resistance is equal to the average of the individual resistances
C. The total resistance is more than the largest resistor
D. The total resistance is in between the smallest and largest resistor but not the average of the individual resistances

Answer

To solve the question about four unequal resistors connected in parallel and determine which statement is correct, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Parallel Connection**:
- In a parallel circuit, the voltage across each resistor is the same, while the total current is the sum of the currents through each resistor.

2. **Identifying Resistors**:
- Let the resistors be R1, R2, R3, and R4.

3. **Applying Ohm's Law**:
- According to Ohm's Law, the current through each resistor can be expressed as:
- I1 = V/R1
- I2 = V/R2
- I3 = V/R3
- I4 = V/R4
- Where V is the common voltage across all resistors.

4. **Total Current Calculation**:
- The total current (I) flowing from the source is the sum of the currents through each resistor:
- I = I1 + I2 + I3 + I4
- Substituting the expressions for I1, I2, I3, and I4, we get:
- I = V/R1 + V/R2 + V/R3 + V/R4

5. **Expressing Total Current in Terms of Equivalent Resistance**:
- The total current can also be expressed using the equivalent resistance (R_eq):
- I = V/R_eq
- Equating the two expressions for total current gives:
- V/R_eq = V/R1 + V/R2 + V/R3 + V/R4

6. **Cancelling Voltage**:
- Since V is common and non-zero, we can cancel it from both sides:
- 1/R_eq = 1/R1 + 1/R2 + 1/R3 + 1/R4

7. **Finding Equivalent Resistance**:
- Rearranging gives us the formula for equivalent resistance in parallel:
- R_eq = 1 / (1/R1 + 1/R2 + 1/R3 + 1/R4)

8. **Analyzing the Result**:
- The equivalent resistance (R_eq) will always be less than the smallest individual resistor in the parallel connection. This is a key property of resistors in parallel.

9. **Conclusion**:
- Therefore, the correct statement is that the total resistance (R_eq) is less than the smallest resistor among R1, R2, R3, and R4.