http://www.ck12.org Chapter 14. Electric Circuits Version 2
Ohm’s Law and Total Quantities
Ohm’s law is the main relationship for electric circuits but it is often misused. In order to calculate the voltage drop
across a light bulb — or any single resistor — use the formula:
Vlightbulb=IlightbulbRlightbulb.
Using the formulas and the rules above, a circuit with any number of resistors (and voltage sources) can be modeled
as a circuit with just one voltage source and one resistor, for which Ohm’s Law also holds. For thetotalcurrent
flowing out of the power source, you need thetotalresistance of the circuit and thetotalcurrent:
Vtotal=ItotalRtotal [7]This concept is illustrated below.
Example on Circuit Math
Question:Analyze the diagram below.
a) Find the current going out of the power supply.
b) How many Joules per second of energy is the power supply giving out?
c) Find the current going through the 75Ωlight bulb.
d) Order the light bulbs in terms of brightness.
e) If the light bulbs were all wired in parallel, order them in terms of brightness.
Answer
a) To find the current going out of the power supply, we will use equation [7],Vtotal=ItotalRtotal. We already have
the total voltage drop(120V)and we are trying to solve for the current. This means that we need to know the total
resistance before we can find the current.
To solve for the resistance we will apply the two rules for resistors (series and parallel) because we have both in
are circuit. First, we must combine the two resistors in parallel so that we can treat the entire circuit as a series.
According to equation [6],
1
Rpar==1 75 Ω+ 1
45 Ω= 3375120 Ω
Because 3375120 Ωis equal toR^1