Two identical resistors each of resistance 10 ohm are connected in:
(i) Series, (ii) Parallel, in turn to a battery of 6V.
Calculate the ratio of power consumed by the combination of resistor in the two cases.
30656"


Given:

Two resistances of 10 ohm each are connected in Series and then Parallel.

Voltage = 6 V.

To find: The ratio of power consumed in the two cases

Solution:

We know power consumed by a resistor $ = \frac{Voltage^2}{Resistance}$

Or 

$P = \frac{V^2}{R}$

Series case:

Effective Resistance R = R1 + R2

= 10 + 10

So effective resistance R = 20 ohm

Power $P = \frac{V^2}{R}$

$= \frac{6^2}{20} = 1.8$

Power = 1.8 watt


Parallel case:

We can find effective resistance using the formula

$\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2}$

$\frac{1}{R} = \frac{1}{10} + \frac{1}{10}$

$\frac{1}{R} = \frac{2}{10}$

So effective resistance, $R = \frac{10}{2}$

= 5 ohm

Power $P = \frac{V^2}{R}$

$= \frac{6^2}{5} = 7.2$

Power = 7.2 watt


Ratio of power in the given cases  = $\frac{1.8\ watt}{ 7.2 \ watt}$
=  $\frac{1}{4}$

So ratio of power consumed is $\frac{1}{4}$

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Updated on: 10-Oct-2022

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