Derive equivalent resistance of a series connection and the parallel connection​ of three resistors

Answers (1)
S safeer

Resistors in series

The potential difference V=V1+V2+V3

Since current flowing is the same

\\V=IR_1+IR_2+IR_3

If the total resistance of the circuit is R then V=IR, therefore

\\IR=IR_1+IR_2+IR_3\\or\ R=R_1+R_2+R_3

The net resistance in series combination is the sum of the resistors. 

Resistance in parallel

In a parallel circuit, the voltage across the resistors remains the same but the current get distributed. That is 

\\I=I_1+I_2+I_3

If R is the total resistance of the circuit then 

\\I=\frac{V}{R}

Therefore

\\\frac{V}{R}=\frac{V}{R_1}+\frac{V}{R_2}+\frac{V}{R_3}\\or\ \frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}

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