Equivalent Resistors
Introduction
The circuits in this set of problems consist of several resistors and an ohmmeter. The resistors are
connected together to form a “resistor subcircuit”. The ohmmeter measures the equivalent
resistance of the resistor subcircuit.
These circuits can be simplified by repeatedly replacing series or parallel resistors by an
equivalent resistor. Eventually, the resistor subcircuit is reduced to a single equivalent resistor.
The ohmmeter measures the resistance of that single equivalent resistor.
(What is a “subcircuit”? It’s part of a circuit. What is the “equivalent resistance” of a resistor
subcircuit? When we reduce the resistor subcircuit to a single equivalent resistor as described
above, the equivalent resistance is the resistance of the equivalent resistor.)
Series resistors are discussed in Section 3.4 of
Introduction to Electric Circuits
by R.C. Dorf and
J.A Svoboda.
Parallel resistors are discussed in Section 3.5. Equivalent resistance is described in
Section 3.7.
Worked Examples
Example 1:
Consider the circuit shown in Figure 1. Find the value of the resistance
R
.
Figure 1
The circuit considered in Example 1.
Solution:
The terminals in Figure 1 divide the circuit into two parts, the part to the left of the
terminals and the part to the right of the terminals. The part to the left of the terminals consists of
1
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 Spring '08
 JUANG
 Resistor, Electrical resistance, Series and parallel circuits, equivalent resistor, J.A Svoboda, R.C. Dorf

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