Question

derive an expression for resultant resistance of series combination of resistors

Answer 1

Answer:

• In series combination, resister are connected end to end and current has a single path through the circuit but the potential difference varies across each resistor. Thus we can write as,
• V = V1 + V2 + V3
• according to Ohm's law V = IR So,  
• V1 = I R1, V2 = I R2, V3 = I R3
• V = I R1 + I R2 + I R3
• V = I(R1+R2+R3)
• V =IRe
• All the individual resistances become equal to the equivalent resistance.
• ​or Re = R1 + R2 + R3......Rn
• In parallel combination, each resistor'sone is connected to the positive terminal while the other end is connected to a negative terminal. The potential difference across each resistance is the same and the current passing through them is different.
• V = V1 =V2=V3
• I  = I1+ I2+I3
• Current throught each resistor will be:
• I1= V/R1 , I2 = V/R2 = I3 = V/R3
• I = V (1/R1+ 1/R2+1/R3)  
• In case of equivalent resistance I=V/Re
• V/Re =  V (1/R1+ 1/R2+1/R3)
• So the equivalnet resistance is the sum of all resistances
•   1/Re = 1/R1+ 1/R2+1/R3

Answer 2

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