Question

Two bulbs of equal power are connected in parallel and they totally consume $110\,W$ at $220\,V$. The resistances of each bulb is:
A. $550\,\Omega$
B. $440\,\Omega$
C. $330\,\Omega$
D. $880\,\Omega$
E. $660\,\Omega$

Answer 1

In this solution, first find total amount of power output and then using power formula for voltage and resistance ($P = \dfrac{{{V^2}}}{R}$) to find the required answer.

Complete step by step solution:
We have,
$P = 110W$
$V = 220\,V$

Bulbs are connected in parallel and they totally consume $110\,W$ at $220\,V$.
Here, Total power, ${P_{total}} = {P_1} + {P_2}$
So, $P + P = 110\,{\rm{W}}$
Where, ${P_1} = {P_2} = P$
So,
$\begin{array}{l} \Rightarrow 2P = 110\,{\rm{W}}\\\ \Rightarrow P = 55\,{\rm{W}}\end{array}$
We know that,
Power formula,
$\begin{array}{c}P = \dfrac{{{V^2}}}{R}\\\55 = \dfrac{{{{\left( {220} \right)}^2}}}{R}\\\R = \dfrac{{{{\left( {220} \right)}^2}}}{{55}}\end{array}$
$\begin{array}{c}R = \dfrac{{220 \times 220}}{{55}}\\\ = 880\,\Omega \end{array}$

Hence, the required answer is $880\,\Omega$, option D.

Additional information:
Resistance: Resistance is a measure of the opposition to current flow in an electrical circuit (also known as ohmic resistance or electrical resistance). Ohms measure resistance, symbolized by omega $\Omega$. The electrical current passes through it when a voltage is applied to a surface. The voltage applied in the material is proportional to the current. Resistance is the constant of proportionality. Resistance is therefore defined as the ratio of voltage added through the substance to the current.

Power: Power is the quantity of energy per unit time that is transmitted or transformed in physics. Power is a scalar number. The power of the engine is the product of the torque generated by the engine and the angular speed of the direction of the engine shaft.

Formula,
For voltage and current: $P = V \times I$
For current and resistance: $P = {I^2}R$
For voltage and resistance: $P = \dfrac{{{V^2}}}{R}$

Note: For every numerical different type formula is used like, voltage and current ($P = V \times I$), current and resistance ($P = {I^2}R$) and voltage and resistance ($P = \dfrac{{{V^2}}}{R}$), so use choosing correct formula is important.
As in an electrical circuit, when the voltage remains the same. Current rises as resistance decreases and current decreases as resistance increases. Present bypassed appliances eliminate resistance.