P=(vR1R2)/(R1+R2)^2 maximum power?

Question

The electric power  P in watts in a direct-current circuit with two resistors R1 and R2 connected in series is P=(vR1R2)/(R1+R2)^2 where v is the voltage. If v and R1 are held constant, what resistance R2 produces maximum power?

Please Help! Theres a quiz grade riding on this

Answer 1

elektrik stuf: power=volts*amps=watts

amps=volts/resistans, so power=volts^2/resistans

if hav 2 resisters in seerees, yu add the 2 resistanses

Answer 2

Question: The electric power  P in watts in a direct-current circuit with two resistors R1 and R2 connected in series is P=(vR1R2)/(R1+R2)^2 where v is the voltage. If v and R1 are held constant, what resistance R2 produces maximum power?

v and R1 are held constant, therefore P is a function of R2 only. Thus we have,

P(R2) = C1.R2/(C2+R2)^2

where C1 and C2 are constants and C1 = vR1 and C2 = R1.

Differentiate P wrt R2 and set to zero.

dP/dR2 = C1/(C2 + R2)^2 - 2C1.R2/(C2 + R2)^3 = 0

{C1.(C2 + R2) - 2C1.R2}/(C1 + R2)^3 = 0

C1.(C2 + R2) - 2C1.R2 = 0

C2 + R2 - 2R2 = 0

C2 = R2

i.e. R1 = R2  (since C2 = R1)

Power is at a maximum when R2 = R1

Answer 3

11-2r^2+r^2

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r^2-3