Conceptual Physics

Derivation

Variables

Strategy

1. Find the total current flowing through all the resistors combined.


2. Use Ohm’s law to rewrite the current in terms of potential difference and
   resistance. An algebraic simplification gives the parallel rule for resistors.

Physics principles and equations

Since charge is conserved, the current flowing out of a junction equals the sum of the

currents flowing into the junction.

Ohm’s law

ǻV = IR

The potential difference is the same across all parallel branches.

Step-by-step derivation

What is the equivalent resistance

of these resistors and what is the

current at the point shown?

current through circuit Itotal

current through ith resistor Ii

potential difference across all resistors ǻV

potential difference across ith resistor ǻVi

equivalent resistance of circuit Requiv

resistance of ith resistor Ri

Step Reason

1. Itotal = I 1 + I 2 + ... + In conservation of charge

2. Ohm’s law

3. potential differences equal

4. divide by equal potential

difference

27.11 - Interactive problem: a parallel circuit

The circuit contains a battery and three light bulbs. The resistance of two of the light

bulbs is known. Your task is to determine the resistance of the third light bulb.

You have an ammeter. It can be placed anywhere in the circuit to determine the

current at that point. Use the ammeter, along with your knowledge of parallel circuits

and Ohm’s law, to determine the resistance R.

Type your answer in the space provided. Press CHECK to see if your answer is

correct. You can try again by entering a new value and pressing CHECK again.

Central to solving this problem is the nature of potential difference and equivalent

resistance in parallel circuits. You also need to calculate the equivalent resistance

for resistors arranged in series, and apply Ohm’s law. Review the sections of the

textbook on these topics if you are having trouble.

(^496) Copyright 2000-2007 Kinetic Books Co. Chapter 27