Question

Write the expression for net resistance of two resistors when they are connected in

(a) Series (b) Parallel​

Answer 1

Series combination:

In this type of combination of resistors, the resistors are connected end to end similar to a series. The current flowing though each conductor remains same. Voltage differs in each of the resistors. It depends upon the resistance of each resistor. So, Let's derive the expression for net resistance in series combination.

↘️ Refer to attachment-1

• Resistors are connected in series
• A battery of voltage V is used.
• Let the Resistors be R1, R2 and R3
• Let the voltage across each resistors be V1, V2 and V3

Sum of potential difference

➝ V = V1 + V2 + V3.....

Applying ohm's law,

➝ IR = IR1 + IR2 + IR3.....

➝ IR = I(R1 + R2 + R3....)

➝ R = R1 + R2 + R3......

Required expression,

$\large{ \therefore{ \boxed{ \sf{R = R_1 + R_2 + R_3.....}}}}$

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Parallel combination:

In this type of combination, the resistors are connected between same two points. The potential difference across each resistors is the same. The current flowing through each resistor is different and depends upon the resistor. So, Let's derive the Express for total resistance.

↘️ Refer to the attachment-2

• Here are three resistors connected in parallel.
• Potential difference = Applied voltage
• Let the current flowing through each resistor be I1, I2 and I3
• And resistors be R1, R2, R3.

Sum of Current flowing,

➝ I = I1 + I2 + I3....

Applying Ohm's law,

➝ V/R = V/R1 + V/R2 + V/R3...

➝ V/R = V( 1/R1 + 1/R2 + 1/R3....)

➝ 1/R = 1/R1 + 1/R2 + 1/R3....

Required expression,

$\large{ \therefore{ \boxed{ \sf{ \frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} .....}}}}$

☀️ Hence, derived !!

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