If resistors R1, R2, and R3 are connected in parallel to a battery of voltage V, then the expression for the equivalent resistance is;

A
$\frac{1}{R} = \frac{1}{R_{1}} + \frac{1}{{R_{2}}_{}} + \frac{1}{_{} R_{3}}$
B
$R = \frac{1}{R_{1}} + \frac{1}{{R_{2}}_{}} + \frac{1}{_{} R_{3}}$
C
$\frac{1}{R} = \frac{1}{R_{1}} - \frac{1}{{R_{2}}_{}} + \frac{1}{_{} R_{3}}$
D
None of the above

Solution:

\frac{1}{R} = \frac{1}{R_{1}} + \frac{1}{{R_{2}}_{}} + \frac{1}{_{} R_{3}}

.
If one end of all the resistors is connected to one point and the other ends of all the resistors are connected at another point, then the resistors are said to be connected in parallel. Therefore, the potential difference between each resistor will be equal. Different currents will flow if the resistance of each resistor varies. As shown in the following diagram,

Current in the main

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

Individual resistor current are

I_{1} = \frac{V}{R_{1}}

I_{2} = \frac{V}{R_{2}}

, and

I_{3} = \frac{V}{R_{3}}

We know that potential difference

V

is same across each resistor in parallel combination.
And

I = \frac{V}{R}

Now total current

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

….(1)
Put the values of

I_{1}

I_{2}

and

I_{3}

in (1) we get

\Rightarrow \frac{V}{R} = \frac{V}{R_{1}} + \frac{V}{R_{2}} + \frac{V}{R_{3}}

\Rightarrow \frac{1}{R} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}}

If resistors R1, R2, and R3 are connected in parallel to a battery of voltage V, then the expression for the equivalent resistance is;

Solution:

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