Question

You measure the power delivered by a battery to be 4.26 W when it is connected in series with two equal resistors. How much power will the same battery deliver if the resistors are now connected in parallel across it

Answer 1

The power delivered by the battery is 17.04 W

Step-by-step explanation:

Power through a circuit is given as

P = IV ....1

where P is the power

I is the current through the circuit

V is the voltage through the circuit

The voltage in a circuit is given as

V = IR ....2

Let us take the value of each resistor as equal to R

when connected in series, the total resistance will be

`R_(t)` = R + R = 2R

If we assume constant voltage through the circuit, then from equation 2, the current in this case is

I = V/2R

If the resistors are connected in parallel, then the total resistance will be

`(1)/(R_(t) )` =
`(1)/(R)` +

`R_(t)` = R/2

The current in this case will be increased since the resistance is reduced

I = 2V/R

comparing the two situations, we can see that the current increased when connected in parallel to a ratio of

`(2V)/(R)` ÷
`(V)/(2R)` =

This means that the current increased 4 times

From equation 1, we can see that electrical power is proportional to the current at a constant voltage, therefore, the power will also increase by four times to

P = 4 x 4.26 = 17.04 W