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Found in: Page 775

College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

(a) What is the resistance of ten ${\mathbf{275}}{\mathbf{-}}{\mathbf{\Omega }}$resistors connected in series? (b) In parallel?

(a)The resistance of ten $275\Omega$resistors connected in series is $2750\Omega$.

(b)The resistance of ten $275\Omega$ resistors connected in parallel is $27.50\Omega$.

See the step by step solution

Step 1: Definition of resistance in series and parallel

An unwillingness to accept anything, such as a change or a new thought, is known as resistance.

Resistance in series: When resistors are daisy-chained together in a single line and a common current flows through them, they are said to be connected in series.

Resistance in parallel: In a parallel circuit, the total resistance is always less than any of the branch resistances. The total resistance in the circuit decreases when more parallel resistances are added to the lines.

Step 2: Finding resistance of resistors connected in series

(a)

The equivalent resistance of the n resistors with each of resistance and connected in series can be expressed as,

${\mathrm{R}}_{\mathrm{s}}=\mathrm{nR}$

Therefore, substituting the given data, we will get,

${R}_{s}=10×275\phantom{\rule{0ex}{0ex}}=2750\Omega$

Thus, the resistance of ten $275\Omega$ resistors connected in series is $2750\Omega$.

Step 3: Finding resistance of resistors connected in parallel

(b)

The equivalent resistance of the n resistors with each of resistance and connected in parallel can be expressed as,

${\mathrm{R}}_{\mathrm{P}}=\frac{\mathrm{R}}{\mathrm{n}}$

Therefore, substituting the given data, we will get,

${\mathrm{R}}_{\mathrm{P}}=\frac{275\mathrm{\Omega }}{10}\phantom{\rule{0ex}{0ex}}=27.50\mathrm{\Omega }$

Hence, the resistance of ten$275\Omega$resistors connected in parallel is$27.50\Omega$.