When two resistances are connected in parallel, the total current supplied to the circuit divides between the two resistances. The amount of current passing through each resistor depends on its resistance.
Key Concept:
• The current passing through a resistor in a parallel combination is inversely proportional to its resistance.
• Ohm's law (I=V/RI = V / R) applies, where the voltage (VV) across both resistors in a parallel combination is the same. Thus, I1=V/R1I_1 = V / R_1 and I2=V/R2I_2 = V / R_2.
Explanation:
1. Resistors in parallel:
o Suppose two resistors R1R_1 and R2R_2 are connected in parallel.
o The total current II is divided into I1I_1 and I2I_2, where I1I_1 flows through R1R_1, and I2I_2 flows through R2R_2.
2. Current division rule:
o The voltage across both resistors is the same in parallel.
o Using Ohm’s law, I1=V/R1I_1 = V / R_1 and I2=V/R2I_2 = V / R_2.
o Therefore, I1I2=R2R1\frac{I_1}{I_2} = \frac{R_2}{R_1}, which shows that the currents are inversely proportional to the resistances.
Conclusion:
The current divides itself in the inverse ratio of the resistances in a parallel combination.
Final Answer:
(A) In the inverse ratio of resistance
