Electrical power

Question

You are given several identical resistances each of value R = 10Ω and each capable of carrying maximum current of 1 ampere. It is required to make a suitable combination of these resistances to produce a resistance of 5Ω which can carry a current of 4 amperes. The minimum number of resistances of the type R that will be required for this job

Moderate

Solution

Suppose n resistors are used for the required job. Suppose equivalent resistance of the combination is R' and according to energy conservation its current rating is $\mathrm{i}\text{'}.$

Energy consumed by the combination = n x (Energy consumed by each resistance)

$\Rightarrow i{\text{'}}^{2}{\mathrm{R}}^{\mathrm{\prime}}=\mathrm{n}\times {\mathrm{i}}^{2}\mathrm{R}\Rightarrow \mathrm{n}={\left(\frac{{\mathrm{i}}^{\mathrm{\prime}}}{\mathrm{i}}\right)}^{2}\times \left(\frac{{\mathrm{R}}^{\mathrm{\prime}}}{\mathrm{R}}\right)={\left(\frac{4}{1}\right)}^{2}\times \left(\frac{5}{10}\right)=8$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Download Now