Question

A filament bulb $500W, 100V$ is used in a $230V$ main supply. When a resistance$R$ is connected in series, it works perfectly and the bulb consumes $500W$. The value of R is given as
$\begin{align}
  & A.26\Omega \\
 & B.13\Omega \\
 & C.236\Omega \\
 & D.46\Omega \\
\end{align}$

Answer 1

Hint: As they are connected in series, the value of total resistance will be the same. And then the maximum power should be calculated. Then the ohm's law is applied. These all are used to solve this question.

Complete step by step answer:
Ohm's law is a law that states that ‘the voltage across a resistor is directly proportional to the current flowing through the resistance’. Ohm's law is named after the German physicist Georg Ohm (1789-1854). This is a simple equation. Ohm's law is used to conclude the relationship of current, voltage, and resistance. The ohm is described as an electrical resistance among two points of a conductor when a certain potential difference of one volt which is applied to these points generates a current of one ampere in a current carrying conductor. Here as already mentioned,
$R=r$
Maximum power generated is given as,
${{P}_{\max }}=\dfrac{{{E}^{2}}}{4r}$
And also power can be written as,
$P=V\times I$
Therefore the current can found by rearranging,
$I=\dfrac{P}{V}=\dfrac{500}{100}=5A$
Now according to ohm's law,
$V=I\times R=\left( 230-100 \right)=5R$
Therefore after the calculation, the value of resistance is given as
$R=26\Omega $

Hence the correct answer in the option is given as option A.

Note:
In physics, power is the rate of change of energy transferred or converted per unit time. In the International System of Units, the unit of power is fixed as watt which is equal to one joule per second. The output power of a motor will be the product of the torque that the motor produces and the angular velocity of its output shaft.