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Q1PE

Expert-verifiedFound in: Page 775

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 $.

**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.**

**(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\times 275\phantom{\rule{0ex}{0ex}}=2750\Omega $

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

**(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 $.

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