Finding Rate of Energy Loss in an RC Discharge Circuit

AI Thread Summary
To find the rate of energy loss in an RC discharge circuit with R = 2.5 x 10^4 ohms, C = 40 microfarads, and an initial voltage of 25 V, the charge at time t can be calculated using Q = Q(initial)e^(-t/RC). The energy stored in the capacitor is given by U = 0.5 Q^2/C. To determine the rate of energy loss, the derivative dU/dt must be computed, which involves substituting Q(t) into the energy equation and differentiating. Evaluating this expression at t = 0.5 seconds will yield the desired rate of energy loss. This approach effectively combines the principles of charge decay and energy calculations in an RC circuit.
lha08
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Homework Statement


In an RC discharge circuit, R= 2.5 X10^4 ohms and C=40 microfarad. The initial potential difference across C is 25 V. Find the rate at which energy is being lost by C at 0.5 seconds.


Homework Equations





The Attempt at a Solution


Like in this case, I probably have to use Q = Q(initial)e^(-t/RC) and U= 0.5 Q^2/C. But then we need dU/dt...i'm not sure what to do...like i can solve for the charge at t=0.5 seconds and also the current if that matters...but like how am i supposed to use dt?...I've been stuck on this problem for like an hour...
 
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Put Q(t) that you know in the equation for U, then take the derivative. Evaluate the expression that you get at t = 0.5 s.
 
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