we are going to discuss parallel circuits
When, a number of resistors are connected in such a way, that both the ends of individual resistors are connected together
and two terminals are brought out for connection to other parts of a circuit
then the resistors are called, connected in parallel. Here, these terminals of R1, R2, and R3 are connected together
and these opposite terminals of them are connected together. Now, we can say these are connected in parallel
Voltage V is connected across the three resistors, R1, R2, and R3
The total current, drawn from the battery, is I. This current, gets passed through, R1, R2, and R3
Hence, this current gets divided into three parts, I1, I2, and I3
I1, flows through R1, I2 flows through R2, and I3 flows through R3
Obviously, I equals I1 plus I2 plus I3. As voltage, V, is appearing across each of these three resistors
applying, ohm's law we can write, I equals I1 plus I2 plus I3 equals V by R1, plus V by R2, plus V by R3
Say this is equation, 1. Let us consider, the equivalent resistance of these three resistors connected in parallel across terminals, A, and, B, is R, as shown
From this circuit, we can write, I equals V by R. Say this is equation, 2
From 1, and 2, we get, V by R equals V by R1, plus V by R2, plus V by R3
Now, by cancelling V, in both sides we get, 1 by R equals 1 by R1, plus 1 by R2, plus 1 by R3
In general, instead of 3, if there were, n number of resistors connected in parallel, the reciprocal of equivalent resistance, would be, 1 by R equals 1 by R1, plus 1 by R2, plus 1 by R3, plus dot dot dot up to 1 by, Rn
Hope, you got an idea. Thank you