math

posted by .

The equation P=240I-8I^2 represents the power, P, (in watts) of a 240 volt circuit with a resistance of 8 ohms when a current of I amperes is passing through the circuit.

Find the maximum power (in watts)that can be delivered in this circuit.


I had posted this question before, and someone gave me this solution:
- 8 i^2 + 240 i = P

i^2 - 30 i = - P/8

i^2 - 30 i +(30/2)^2 = -P/8 + 225

(i-15)^2 = -P/8 + 225

vertex at i = 15 and P at 225*8 = 1800


From this part on, I don't really get it:
i^2 - 30 i +(30/2)^2 = -P/8 + 225

(i-15)^2 = -P/8 + 225

vertex at i = 15 and P at 225*8 = 1800

Can anyone please explain it to me???THANKS A LOT!

  • math -

    There are two ways to do this kind of problem. One is to use calculus, which leaves you with the equation
    2I - 30 = 0, leading right away to I = 15. The other way, which does not require calculus, is to use the method of "completing the square". That is what was done in the example you posted. When the equation
    P = 240I-8I^2 is rewritten
    I^2 - 30 I +(30/2)^2 = -P/8 + 225
    = (I-15)^2 , or
    P/8 = 225 -(I - 15)^2
    you see right away that the maximum value of P is obtained when I = 15.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    The equation P=240I-8I^2 represents the power, P, (in watts) of a 240 volt circuit with a resistance of 8 ohms when a current of I amperes is passing through the circuit. (a)Find the maximum power (in watts)that can be delivered in …
  2. Math

    The equation P=240I-8I^2 represents the power, P, (in watts) of a 240 volt circuit with a resistance of 8 ohms when a current of I amperes is passing through the circuit. Find the maximum power (in watts)that can be delivered in this …
  3. beginning algebra

    In an electrical circuit, the current passing through a conductor varies inversely with the resistance. Suppose that when the current is 8A (amperes), the resistance is 15 ohms. What is the current when the resistance is 4 ohms?
  4. Physics

    In an electrical circuit, the current passing through a conductor varies inversely with the resistance. Suppose that when the current is 8A (amperes), the resistance is 15 ohms. What is the current when the resistance is 4 ohms?
  5. Intermediate Algebra

    The amount of current flowing into an electrical circuit varies inversely as the resistance in the circuit. When the resistance of a particular circuit is 5 ohms, the current is 42 amperes. what is the current when the resistance is …
  6. Math

    The power P delivered to a load by a current of i amperes through a resistance of 19 ohms, when 110 volts are supplied at one end of the line, is given by the formula P = 110i - 19i2 . Determine the maximum power that can be delivered. …
  7. Math Max min problems

    The power P delivered to a load by a current of i amperes through a resistance of 19 ohms, when 110 volts are supplied at one end of the line, is given by the formula P = 110i - 19i2 . Determine the maximum power that can be delivered. …
  8. Algebra

    The power in an electric circuit varies inversely with the resistance. If the power is 1200 watts when the resistance is 12 Ohms, find the power when the resistance is 6 Ohms.
  9. Physics

    A circuit consists of a resistor of R=7 Ω, a capacitor of C=7 μF, and an ideal self-inductor of L=0.04 H. All three are in series with a power supply that generates an EMF of 5sin(ωt) Volt. The internal resistance of …
  10. Science

    A current of 6.0 amps passes through a motor that has a resistance of 5.0 ohms. Calculate the power 30 watts 150 watts 180 watts *** 900 watts Thanks

More Similar Questions