Question

The electric power P​ (in W) produced by a certain battery is given by:

P= 49r/ (r+0.8)^2​, where r is the resistance in the circuit. For what value of r is the power a​ maximum?

Answer 1

r = 1 Ohms

Step-by-step explanation:

Given that:

P =
`(49r)/((r+0.8)^(2) )`

where r is the resistance in the circuit.

If r = 1 Ohms;

P =
`(49(1))/((1+0.8)^(2) )`

=
`(49)/(1.8^(2) )`

=
`(49)/(3.24)`

= 15.1235

P = 15.12 W

If r = 3 Ohms;

P =
`(49(3))/((3+0.8)^(2) )`

=
`(147)/(14.44)`

P = 10.18 W

If r = 5 Ohms;

P =
`(49(5))/((5+0.8)^(2) )`

=
`(245)/(33.64)`

= 7.230

P = 7.23 W

Therefore, the value of r for maximum power is 1 Ohms.