Question

State Ohm’s law. Write formula for the equivalent resistance R_p of the parallel combination of three resistors of values R₁, R₂ and R₃.

Answer 1

Step 1: Ohm's Law:
Ohm's law states that the current flowing through a conductor is directly proportional to the voltage applied across it and inversely proportional to its resistance. Mathematically, it is expressed as:
\[ V = I \times R \] where:
- V is the voltage across the conductor (in volts),
- I is the current flowing through the conductor (in amperes),
- R is the resistance of the conductor (in ohms).

Step 2: Formula for the equivalent resistance of resistors in parallel:
For three resistors with values R₁, R₂, and R₃ connected in parallel, the equivalent resistance Rₚ is given by the formula: \[ \frac{1}{Rₚ} = \frac{1}{R₁} + \frac{1}{R₂} + \frac{1}{R₃} \] This formula shows that the reciprocal of the total (equivalent) resistance is the sum of the reciprocals of the individual resistances.

Step 3: Conclusion:
- Ohm's law relates the voltage, current, and resistance in an electrical circuit: V = I × R.
- The formula for the equivalent resistance of three resistors in parallel is 1/Rₚ = 1/R₁ + 1/R₂ + 1/R₃.