The Combined Resistance of Parallel Circuits
المؤلف:
GEORGE A. HOADLEY
المصدر:
ESSENTIALS OF PHYSICS
الجزء والصفحة:
p-389
2025-12-11
19
is always less than that of either circuit alone. The reason for this is evident when we consider the expression for the resistance of a wire, 
The putting of two wires in parallel, in place of one of them, is equivalent to increasing the diameter of that one.
FIG .1
Demonstration. - Wind a coil of iron wire No. 18 and couple its ends to two binding posts A and B, Fig. 1. Measure its resistance. Wind a second coil of No. 18 copper wire, couple it to A and B and measure its resistance. Couple both coils to A and B and measure the combined resistance. The last resistance will be less than either of the others.
A careful study of the results of the above demonstration will help the student to understand the conditions which govern the resistance of parallel circuits.
To find an expression for the combined resistance of a circuit and its shunt, we can take the case of a galvanometer with its shunt (Fig. 1).
The current passing through the galvanometer may be written G=V/g , in which G is the current, g the resistance of the galvanometer V and the potential difference at its terminals. The current through the shunt may be written S=V/s.
The entire current will be I=V/R in which R is the combined resistance of the galvanometer and its shunt.
In general, the parallel resistance of two circuits is the product of the two resistances divided by their sum. The parallel resistance of several circuits is found by finding the value of R in the expression
In the case of any number of equal resistances, incandescent lamps for example, the parallel resistance of n lamps is 
th the resistance of a single lamp.
The arrangement shown in Fig. 2 is frequently used when we wish to measure a current greater than the galvanometer will carry safely. A shunt that will carry 
of the current, so that the galvanometer will read 
of the true value of the current, is called a tenth shunt.
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