Question

Two resistors of resistance R and $2R$ are connected in series in an electric circuit. The ratio of the electric power consumed by R and $2R$ is
a. $1:4$
b. $4:1$
c. $1:2$
d. $2:1$

Answer 1

Hint : Current in the resistors which are connected in series is the same. Power consumed by a resistor of resistance R
$P={{I}^{2}}R$
Where I = currently in Resistor.

Complete Step By Step Answer:
Let say current in the circuit is I. Here resistors are connected in series so the current will be some in both resistors.

We know that power consumed by a resistor $P={{I}^{2}}R$
therefore power consumed by resistor R, ${{P}_{1}}={{I}^{2}}R$
same for resistor $2R$ .
${{P}_{2}}={{I}^{2}}\left( 2R \right)$
Now the ratio. $\dfrac{{{P}_{1}}}{{{P}_{2}}}=\dfrac{{{I}^{2}}R}{{{I}^{2}}\left( 2R \right)}=\dfrac{1}{2}$
Hence the ratio of electric power consumed by R and $2R=1:2$

Note :
Student solve this question with the formula $P=\dfrac{{{V}^{2}}}{R}$
Now here they should keep in mind that in series, the voltage across the resistor is different. So if they are using this formula then they should first calculate the voltage across the resistors.
This formula is better for calculating the power consumed by an individual resistor connected in parallel. Voltage across resistors in parallel is some.