Two identical heater filaments are connected first in parallel and...

Two identical heater filaments are connected first in parallel and then in series. At the same applied voltage, the ratio of heat produced in same time for parallel to series will be:

Options

A $1: 4$
B $4: 1$
C $2: 1$
D $1: 2$

Correct answer

B. $4: 1$

Step-by-step solution

Let the resistance of the filaments be $R and the voltage be$ V $.</p><p>For the series combination the power is </p><p>$ {P}_{1} = $\left(\dfrac{{V}^{2}}{2R}\right)$

For parallel combination,

${P}_{2} = \dfrac{{V}^{2}}{\left(\dfrac{R}{2}\right)} = \left(\dfrac{2{V}^{2}}{R}\right)$

Hence, the ratio is

$⇒ \dfrac{{P}_{2}}{{P}_{1}} = \dfrac{4}{1}$

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