In a circuit, suppose the three resistors having the values 5, 10, 20 N are connected in parallel; then equivalent resistance of the circuit will be ______.

Question

Question

This question was previously asked in

RRB Technician Grade III Official Paper (Held On: 29 Dec, 2024 Shift 1)

Answer 1

The correct answer is (20)/(7) Ω.

Key Points

When resistors are connected in parallel, the reciprocal of the equivalent resistance (R_eq) is the sum of the reciprocals of the individual resistances.
The formula used is: 1/R_eq = 1/R₁ + 1/R₂ + 1/R₃.
For resistors with values 5Ω, 10Ω, and 20Ω, the calculation is: 1/R_eq = 1/5 + 1/10 + 1/20.
Solving the equation: 1/R_eq = (4 + 2 + 1)/20 = 7/20, thus R_eq = 20/7 Ω.

Additional Information

Series vs. Parallel Circuits:
- In a series circuit, resistors are connected end-to-end, and the total resistance is the sum of individual resistances.
- In a parallel circuit, resistors are connected across the same two points, and the total resistance is less than the smallest individual resistance.
Ohm's Law:
- Ohm's Law states that the current through a conductor between two points is directly proportional to the voltage across the two points.
- The formula is V = IR, where V is voltage, I is current, and R is resistance.
Applications of Parallel Circuits:
- Parallel circuits are commonly used in household wiring, allowing multiple devices to operate independently.
- They ensure that if one component fails, the rest of the circuit can still function.
Calculating Total Resistance:
- For multiple resistors in parallel, always use the reciprocal formula to find the total or equivalent resistance.
- This method ensures accurate calculation and understanding of how current divides among different branches.