The same voltage V is impressed on each of the branches of a parallel circuit. The voltage source provides a total current
to the circuit, and ’sees' a total equivalent resistance of R in the circuit. That is,
.Use Ohm’s law
Prove the expression
Explanation of Solution
Given info:
Total current in the circuit is
Current in the first, second, third and nth branch of the circuit is
Resistance in first, second, third and nth branch of the circuit is
Voltage of the circuit is
Formula Used:
Write the expression to calculate the total current of the circuit.
Write the expression to calculate the current through first resistor.
Write the expression to calculate the current through second resistor.
Write the expression to calculate the current through third resistor.
Write the expression to calculate the current through nth resistance.
Write the expression to calculate the total current through circuit.
Calculation:
Substitute the values of currents through resistors in the circuit in the expression of total current through circuit.
Conclusion:
The expression of equivalent resistance
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