Set 53 Problem number 2

Problem

What is the current through the resistors, and how much does the voltage change across each resistor if we have a constant 5 Volt potential difference across series resistances of 48 Ohms and 51 Ohms?

Solution

Since the current must go through both resistors, it will experience the total resistance 48 ohm + 51 ohm = 99 ohm.

• The current must therefore be ( 5 Volts)/( 99 Ohms) = .0505 Amps.
• The voltage change associated with .0505 Amps through 48 ohm is ( .0505 Amps)( 48 ohm) = 2.424 Volts
• Through the 51 ohm resistor the change is ( .0505 Amps)( 51 ohm) = 2.575 Volts.
• Note that these individual voltages add up to the original voltage.

Generalized Solution

When we have two resistors in series, the same current must go through both and their potential differences therefore add (if we go across one, a certain amount of work is done per Coulomb of charge; then when we go across the other an additional amount of work is done per Coulomb; the total is the total voltage across the resistors).  It follows that if the total voltage is V and the resistances are R1 and R2, and the current is I = V / (R1 + R2) and the total resistance must therefore be R1 + R2.

• The voltage drop across each resistor is thus I multiplied by the resistance of that resistor:  V1 = I * R1 and V2 - I * R2.