Physics doubts. Urgent help is needed!?
1) There are two equations for power consumed by a device:
P = I²R
P = V²/R
The first expression indicates that Power is directly proportional to R whereas the second expression indicates inverse proportionality.
How can the seemingly different dependence of P on R in these expressions be explained?
2) An electrician puts a fuse of rating 5A in that part of domestic electrical circuit in which an electrical heater of rating 1.5kW, 220V is operating. What is likely to happen in this case and why? What change, if any, needs to be made?
From ohm’s law,
I = V / R, V = I * R, R = V / I
The equation for power, P = Voltage x Current = V * I
But V = I / R, & substitute the above value in above eqn
P = V * I = (I * R) * I = I² * R ……………(1)
P = V * I = V * (V /R) = V² / R…………(2)
In eqn (1), P is directly proportional to I² & R
In eqn (2), P is directly proportional to V² & inversely to R.
Comparing to the values of V & I , V is much much higher than that of I. Hence, the difference in their squares will be still higher. So in the second equation ,the extra magnitude caused by squaring the V will be neutralised by inverse proportionality of the resistance.
(2) The rating of the heater = 1.5 kw = 1500 w & 220 V
As Power P = V * I, I = P / V
Hence, Current = 1500 / 220 = 6.8 Ampere.
As the fuse is only of 5 A the fuse will blow off. To protect this any value higher than 6.8 Amps ( as a safety margin make it 7 amps)
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