# How can I find the time at which the diode charges the capacitor every cycle(half wave rectifier)

Half wave rectifier is given and given values are :

V_p = 10V, V_d = 0.7V, 1/T = 60Hz, R = 10.

I want to know when C = 0.1F, how can I find the time at which the diode charges the capacitor every cycle.

I failed to approach this problem because I'm not sure at which parameter I should find out. I'm understanding capacitor charging time is T, but I don't think T=1/60 is answer.

I tried so far on this :

$$i_{DMAX} = \frac{V_p-V_d}{R} + C\cdot V_p\cdot \frac{2\pi}{T}\sqrt{\frac{2V_R}{V_p}} = 65.02A$$

$$dv/dt = V_P\cdot \omega \cos(\omega t)$$

---redo---

Now I find when charging time is $$\ \Delta T\$$

$$v_0(T-\Delta T) = V_p-V_d-V_r$$

and

$$V_r =\frac{(V_p-V_d)T}{RC}$$

$$v_0(T-\Delta T) = V_pcos(\frac{2\pi}{T}\Delta T)-V_D$$

• What have you tried so far on this? May 20, 2020 at 15:47
• Please show all of your work and ask a more specific question. This is not Chegg, we won't do your homework for you. May 20, 2020 at 15:53
• I failed to approach this problem because I'm not sure at which parameter I should find out. I'm understanding capacitor charging time is T, but I don't think T=1/60 is answer. May 20, 2020 at 16:17
• The capacitor start be charging when $v_s$ is $v_d$ above the output voltage and stop when it falls below this voltage. Without effort on your part we can't do homework for you. May 20, 2020 at 16:22
• I edited some of the questions, sorry for ambiguous posting. May 20, 2020 at 16:42

[Wrong answer] the capacitor never charges completely, we often calculate the time at which the capacitor will charge to 63% of Vs

First have the charging formula:

$$\begin{eqnarray*} V(t)=V1(1- e^{\frac{-t}{RC}}) \end{eqnarray*}$$

simulate this circuit – Schematic created using CircuitLab

$$$$V(RC)=V1(1- e^{-1})= 0.63\times V1\\$$$$

So now you have your time constant in seconds which is: RC

you still must verifiy a condition on RC, it should be smaller than the priod of your signal

• Since the OP is talking about 60Hz it's a sinusoidal input not DC. Also your formula is for a series resistor, not parallel. May 20, 2020 at 16:23
• The formula is just to show the equation, I know he's asking about AC why the formula is not for parallel? May 20, 2020 at 16:28
• The capacitor charges via the diode and not via the resistor. I suggest you quickly remove this post to save face. May 20, 2020 at 16:31
• With your circuit when you close the switch the R you need to use is that of the switch not the one you have drawn. The capacitor will charge very quickly. May 20, 2020 at 16:31
• Yes yes now I can see what you mean thank you for clarifications May 20, 2020 at 16:40