Physics, 23.01.2020 00:31 blake2001

With two identical light bulbs and two identical batteries how would you arrange in order to get the maximum total power to the light bulbs?

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Answer from: evanmc627

The batteries would be connected in series while the bulbs would be connected in parallel

Explanation:

Power (W) = VI

where V = voltage, I = current and R = resistance

from V = IR , I = V/R

Power (W) now becomes = V (V/R) = $\frac{V^{2} }{R}$

Power (W) = $\frac{V^{2} }{R}$

from the above equation, power is directly dependent on voltage, hence the voltage has to be high for the power to be high and the power is also inversely dependent on the resistance (in this case the bulbs which act as the load)

We have to batteries, when batteries are connected in series the total voltage becomes the summation of the two voltages hence giving a higher voltage and when they are connected in parallel their voltage remains the same. Since we want to get higher voltage we will connect the two batteries in series.we have two bulbs which are the resistance here, from the equation above the power is inversely dependent on the resistance so we would need its value to be minimal. When resistance is connected in series the resistance individual will be added to get the total resistance, hence the total resistance will be high but when the resistors are arranged in parallel you get the total resistance by applying the formula $\frac{R1R2}{R1+R2}$ which will give us a lower resistance. Hence we would connect the bulbs in parallel.

Take note that the power from this connection should not exceed the bulbs power rating so as to avoid damage of the bulbs.

Answer from: Quest

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

$p(t)=0.3t^2+6t+80$

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

$p(0)=0+0+80=80$

according to question, we have said that if the population has twice its initial population, then it becomes

$p(t)=2\times 80=160$

so, time taken to reach this above mentioned population is given by

$160=0.3t^2+6t+80\\\\160-80=0.3t^2+6t\\\\80=0.3t^2+6t\\\\0.3t^2+6t-80=0\\\\\text{using quadratic formula ,we get }\\\\t_{1,\: 2}=\frac{-60\pm \sqrt{60^2-4\cdot \: 3\cdot \: 800}}{2\cdot \: 3}\\\\t=-29.14\ and\ t=9.149$

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.

Answer from: Quest

Ibelieve the answer is b

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