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Math proof problem quick help?
the voltage v of a circuit can be calculated using the formula v=p/i where p is the power and i is the current of the circuit
I need 2 write a proof to show that when the power is constant the voltage is halved when the current is doubled
Also write a proof to show that when the curent is constant, the voltage is doubled when the power is doubled
Any help il appreciate cuz i just dont get dis question
1 Answer
- V. SinghLv 69 years agoFavorite Answer
This is the simple proof, just do it what the question says
original equation we know
P = I*V ; Power = Current * Voltage
1)
Pi = I(initial) * V(initial) ----------1)
Pf = I(final) * V(final) -------------2)
Given that Pi = Pf ( power constant), I(f) = 2* I(i)
I(initial) * V(initial) = I(final) * V(final) ; as P(initial) = P(final)
I(i) * Vi = 2*I(i) * Vf ; cancel out I(i)
Vi = 2 * Vf ; or
Vf = ½ Vi
That mean final Voltage is halved of initial Voltage when current is doubled
----------------------------
Try your self for the second portion. this time current is constant in both the equations
Pi.....Pf
---- = ---- ; now plug the given facts that Pf = 2*Pi (power is doubled)
Vi.....Vf
Pi.....2*Pi
---- = ----
Vi.....Vf
Cancel Pi and solve for Vf = 2* Vi (meaning final voltage is doubled when Power is doubled
Hope this helped
Vick
