Question

derive the equation for equivalent resistance for 3 resistances in series and parallel​

Answer 1

Suppose a current I flows through the circuit when a cell of voltage V is connected across the combination. ... (ii) Total voltage across the combination = Sum of the voltage drops. (iii) Voltage drop across any resistor is proportional to its resistance. (iv) Equivalent resistance = Sum of the individual resistances.

Answer 2

Answer:

(i) Total potential difference across a combination of resistors in series is equal to the sum of potential difference across the individual resistors.

V = V1 + V2 + V3

Let I be the current in the circuit. The current through each resistor is also I. It is possible to replace the three resistors joined in series by an equivalent resistor of resistance R. Applying Ohm's law,

V = IR

On applying Ohm's law to the three resistors respectively we further have

V1 = IR1

V2 = IR2

V3 = IR3

But V = V1+ V2 + V3

IR = IR1 + IR2 + IR3

R = R1 + R2 + R3