Calculating Power Dissipated in 20 Ohm Resistor: I = 12 sin(250t)

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To calculate the power dissipated in a 20-ohm resistor with an electric current described by I = 12 sin(250t), the equation P = I^2 * R is used, yielding P = 2880 sin^2(250t). However, to find the average power dissipated as heat, it is necessary to integrate over a time period and then divide by that period to obtain the root mean square (rms) value. The discussion emphasizes that the problem specifically asks for power dissipated as heat rather than instantaneous power. Clarification on efficiency is not needed since the question does not provide efficiency parameters or a specific time value. The correct approach involves calculating the average power using rms values.
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Homework Statement


An electric current described by I = 12 sin(250t) flows through a 20 ohm resistor. Calculate the power dissipated as heat.


Homework Equations


V=IR
P=IV
P = I^2*R


The Attempt at a Solution


Using the last equation, P = I^2*R
P = 2880 sin^2(250t)
Is that the best answer I can give? The question gives no information about efficency so I'm not sure if I'm forgetting an equation or something. It doesn't give a value for time either.
 
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I think you misinterpreted the problem. The problem asks for the power dissipated as heat, not the power in the element.
 
You need to integrate over a time period then divide by the period to get the root mean square (rms) value.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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