Consider a parallel combination of 3 resistors R₁, R₂ and R₂ with currents I₁, I[2 and I₃, respectively. Which of the following is true? (I = total current, R_eq = equivalent resistance of the circuit)

The correct answer is I = I1 + I2 + I3.

Key Points

• In a parallel circuit, the total current (I) flowing through the circuit is the sum of the currents flowing through each branch. Hence, I = I1 + I2 + I3.
• The voltage across each resistor in a parallel combination is the same, but the current varies depending on the resistance of each branch.
• Ohm's Law (V = IR) is used to calculate the current through each resistor when the resistance and voltage are known.
• In parallel circuits, the total current is distributed among the branches, and this is one of the key characteristics of such circuits.
• The principle of current conservation is applied here, which states that the total current entering a junction equals the total current leaving the junction.
• Parallel circuits are commonly used in electrical systems where components need to operate independently, such as in home wiring systems.

 Additional Information

• R_eq = R3 + (R2R1)/(R2 + R1)
  • This formula is incorrect for calculating the equivalent resistance in a parallel circuit. The correct formula involves the reciprocal of resistances.
  • For two resistors in parallel, the equivalent resistance is given by 1/Req = 1/R1 + 1/R2 + ....
• 1/I = 1/I1 + 1/I2 + 1/I3
  • This equation is incorrect as it misrepresents the relationship between the total current and individual branch currents in a parallel circuit.
  • The reciprocal rule applies to resistances in parallel, not currents.
• R_eq = R1 + (R2R3)/(R2 + R3)
  • This formula is also incorrect as it doesn't represent the correct calculation of equivalent resistance in a parallel circuit.
  • In a parallel circuit, the equivalent resistance is always smaller than the smallest individual resistance.