Physics
How would you connect two resistors in series? Draw a diagram. Calculate the total equivalent resistance.
Answer
Below diagram shows two resistors connected in series:
If current I is drawn from the battery, the current through each resistor will also be I.
By Ohm's law,
p.d. between A and B is V1 = VA - VB = IR1
p.d. between B and C is V2 = VB - VC = IR2
Adding these we get,
V = V1 + V2
= VA - VB + VB - VC
= VA - VC
= IR1 + IR2
= I (R1 + R2) [Equation 1]
If the equivalent resistance between the points A and C is RS, then the potential difference between the points A and C is
V = VA - VC = IRS [Equation 2]
Therefore from equation 1 and 2,
IRS = I (R1 + R2)
⇒ RS = R1 + R2
Thus, in the series combination, the equivalent resistance is equal to the sum of the individual resistances.
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