Question

Consider the power dissipated by the two circuits in the video. The ratio of power dissipation in the parallel circuit to that in the series circuit is:
A) 9

B) 3

C) 1

D) 1/9

E) 1/3

In the video, there are two circuits: one with three light bulbs connected in parallel, and the other with three light bulbs connected in series.

Answer 1

Answer:

A)

Explanation:

• In a series circuit,  if we assume that each bulb has a resistance R, the equivalent resistance, is the sum of all the resistances, in this case, 3*R.
• The power dissipated in this resistance, can be expressed as follows:

       $P_{series} = V*I = V*(\frac{V}{R_{eq}}) = \frac{V^{2}}{3*R} (1)$

• In the parallel circuit, the equivalent resistance, is equal to 1/3*R.

• The power dissipated in this resistance, can be expressed as follows:

       $P_{//} = V*I = V*(\frac{V}{R_{eq}}) = \frac{V^{2}}{\frac{R}{3} } (2)$

• In order to take the ratio of both powers, we can divide both sides of (1) and (2) , as follows:

        $\frac{P_{//} }{P_{series} } =\frac{V^{2}}{\frac{R}{3}} * \frac{3*R}{V^{2}} = 9$

• The ratio of power dissipation in the parallel circuit to that in the series circuit is 9 times.