Question

Two identical resistors, each of resistance 15 ohm, are connected in
(i) series, and (ii) parallel, in turn to a battery of 6 V. Calculate the ratio
of the power consumed in the combination of resistors in each case.​

Answer 1

Answer:

1:4

Explanation:

1. In series resistance 30 ohm
2. in parallel 7.5 ohm

as p=v^2/r

1. power in series 36/30=6/5W
2. power in parallel 36/7.5=24/5

therefore

ratio is 1:4

Answer 2

Given that,

Resistances of the resistors is 15 ohms

Voltage, V = 6 V

To find,

The ratio of the power consumed in the combination of resistors in each case.​

Solution,

Equivalent resistance when two resistors are connected in series :

$R_s=R_1+R_2\\\\R_s=30\ \Omega$

Equivalent resistance when two resistors are connected in parallel.

$\dfrac{1}{R_p}=\dfrac{1}{R_1}+\dfrac{1}{R_2}\\\\\dfrac{1}{R_p}=\dfrac{1}{15}+\dfrac{1}{15}\\\\R_p=7.5\ \Omega$

Power consumed,

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

The ratio of the power consumed,

$\dfrac{P_s}{P_p}=\dfrac{\dfrac{V^2}{R_s}}{\dfrac{V^2}{R_p}}\\\\\dfrac{P_s}{P_p}=\dfrac{\dfrac{(6)^2}{30}}{\dfrac{(6)^2}{7.5}}\\\\\dfrac{P_s}{P_p}=\dfrac{1}{4}$

So, the ratio of the power consumed in each case is 1:4.