Name: Revisiting Ohm's Law & Resistivity
Uploaded: 2019-07-19
Duration: 4 min 5 s
Description: The entire domain of the science of electric current can be explained using Ohm’s law, that’s how powerful this discovery was. We will revise this once again.

Question

With the help of a labelled circuit diagram derive a formula to find combined resistance (R) when two or more resistances $(R_{1}$ , $R_{2}$ , $R_{3} . . . . . . . .)$ are connected in parallel taking symbols potential difference (V) and current (I).

Accepted Answer

Consider resistances $R_{1}$ , $R_{2}$ , $R_{3} . . . . . . . .)$ .... $R_{n}$ are connected in parallel with potential difference $V$ . Let $I$ be the current flows in the circuit as shown in the following diagram.

Let $I_{1}$ , $I_{2}$ , $I_{3}$ ..... $I_{n}$ be the current flowing through the resistances $R_{1}$ , $R_{2}$ , $R_{3}$ ..... $R_{n}$ resistors respectively. I=I1+I2=

According to ohm's law

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

But total current in the circuit is $I = I_{1} + I_{2} + I_{3} + . . . . . . + I_{n}$

Since potential difference across each resistance in the parallel circuit is same

$\frac{V}{R_{e q}} = \frac{V}{R_{1}} + \frac{V}{R_{2}} + \frac{V}{R_{3}} + . . . + \frac{V}{R_{n}}$ ( $R_{e q}$ is the equivalent resistance in the circuit)

The equivalent resistance in the circuit is given by

$\frac{1}{R_{e q}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}} + . . . + \frac{1}{R_{n}}$

Note: The net resistance in the parallel circuit decreases.

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