Question

What is the equivalent resistance in this parallel circuit? Ω What is the voltage in the circuit? V What is the total current in the circuit? A

Answer 1

I=I1+ I2+I3
I= V/R
Voltage remains constant in parallel combination.
V/R = V/R1+ V/R2+V/R3
After cancelling the V from both side,,
1/R= 1/R1+ 1/R2+1/R3

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Answer 2

Explanation:

The expression for the equivalent resistance in the parallel combination is as follows;

$\frac{1}{R}=\frac{1}{R_{1}}+\frac{1}{R_{2}}$

Here, $R,R_{1},R_{2}$ are the resistances.

In the parallel combination of the wire, the amount of the current flowing in the circuit is different but the voltage is same.

If V is the voltage given in the parallel combination of the circuit then V is the voltage across  $R,R_{1},R_{2}$ .

The expression for the total current in the circuit is as follows;

$I=I_{1}+I_{2}+I_{3}$

Here, I is the total amount of current flowing in the circuit, $I_{1},I_{2},I_{3}$ are the current flowing across $R,R_{1},R_{2}$.

Put $I_{1}=\frac{V}{R_{1}}$, $I_{2}=\frac{V}{R_{2}}$ and $I_{3}=\frac{V}{R_{3}}$.

$I=\frac{V}{R_{1}}+\frac{V}{R_{2}}+\frac{V}{R_{3}}$.