RC circuit - Capacitor discharge

[jpas]

When a capacitor discharges, the potential difference between its plates and the resistor's terminals is the same. Hence,

$$\frac{Q}{C}=R \frac{dq}{dt}$$
Solving this equation we get

$$q(t)= Q_{0} exp \frac{t}{RC}$$

Obviously, this isn't the solution. It is actually $$q(t)= Q_0 exp \frac{-t}{RC}$$. So, I'm missing a minus sign on the original equation.

But why should it be there?

 

[intwo]

According to Kirchoff's Second Law, the sum of the voltages is equal to zero. R(dQ/dt) + (Q/C) = 0, therefore you need -R(dQ/dt) = (Q/C). I apologize for the lack of proper script.

 

[jpas]

Thank you.
Didn't know such laws.

 

[willem2]

If the capacitor discharges, then dq/dt is negative, so according toyour originial equation, Q/C which is positive equals something negative

 

[sardar]

As a scientist, it is important to always double check your equations and calculations to ensure accuracy. In this case, the missing minus sign could be due to a mistake in the initial setup of the equation or a miscalculation during the solving process. It is also possible that there is a physical reason for the minus sign to be present.

One possible explanation could be that the negative sign indicates the direction of current flow in the circuit. In an RC circuit, the capacitor initially charges in one direction and then discharges in the opposite direction. Therefore, the negative sign could represent the change in direction of current flow during the discharging process.

Another explanation could be that the negative sign is a result of the choice of direction for the voltage and current variables in the equation. Depending on the convention used, the negative sign may appear or disappear in the final solution.

In any case, it is important to carefully review the physical principles and assumptions behind the equation to determine the appropriate sign to use. It may also be helpful to consult with other experts in the field or conduct further experiments to confirm the correct solution. Overall, as a scientist, it is important to always question and verify our findings to ensure the accuracy and validity of our research.