Question

what will be the equivalent resistance of the number of resistances combined In The parallel arrangement draw the diagram and establish the relation explain in about hundred words

Answer 1

I hope this will help you

Answer 2

$\frac {1}{R_e}=\frac {1}{R_1}+\frac {1}{R_2}+\frac {1}{R_3}+...+\frac {1}{R_n}$

Explanation:

When the resistors are connected in parallel, the potential difference across each resistor is same and equal to the potential provided by the battery. Consider three resistors, $R_1, R_2 and R_3$ connected in parallel combination across potential difference V. Consider  $I_1, I_2, and I_3$ flows in the resistors  $R_1, R_2, R_3$ respectively. Then,

Let R be the equivalent resistance of the circuit and I be the total current.

$I=\frac{V}{R}\\Also,\\I =I_1+I_2+I_3\\I =\frac{V}{R_1}+\frac{V}{R_2}+\frac{V}{R_3}\\\frac{V}{R}=V[\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}]\\\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}$

If there are more resistors connected in parallel, it can be similarly calculated.

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