Capacitor and resistors at t=0 and t after long time

I’m pretty sure my answer is wrong because I forgot to include the capacitor in the calculation and I don't know how I'm supposed to do that. Find the current for each resistor and in the capacitor at t=0 and after a long time. <a href= enter image description here" /> simulate this circuit – Schematic created using CircuitLab \$ \mathrm = \mathrm + \mathrm \$ \$ \begin \mathrm> &= <\left(\frac<\mathrm>+\frac<\mathrm>\right)>^\\ &= <\left(\frac+\frac\right)>^\\ &= 1987.95\Omega \end \$ \$ \begin \mathrm> &= \mathrm + \mathrm>\\ &= 1000 + 1987.95\\ &= 2987.95 \Omega \end \$ \$ \begin \mathrm &= \frac\\ &= 4\!\times\!10^ \mathrm \end \$ \$ \begin \Delta\mathrm &= \mathrm \cdot \mathrm\\ &= 4\!\times\!10^ \cdot 1000\\ &= 4 \mathrm \end \$ \$ \begin \mathrm &= \frac\\ &= 2.42\!\times\!10^\mathrm \end \$ \$ \begin \mathrm &= \mathrm - \mathrm\\ &= 1.58\!\times\!10^\mathrm \end \$

844 1 1 gold badge 5 5 silver badges 15 15 bronze badges asked Apr 4, 2019 at 14:58 11 1 1 silver badge 2 2 bronze badges

\$\begingroup\$ Can you transcribe your work and rotate the image to be the right way up? \$\endgroup\$

Commented Apr 4, 2019 at 14:59 \$\begingroup\$ The voltage on capacitor cannot change instantaneously. \$\endgroup\$ Commented Apr 4, 2019 at 15:08

\$\begingroup\$ Please redraw your circuit using the schematic tool and label each component. This site also uses MathJax so you can write maths so it is easy to read. \$\endgroup\$

Commented Apr 4, 2019 at 15:13

\$\begingroup\$ Also for \$ t = 0 \$ do you mean \$ t = 0^- \$, The switch has been open for a long time or \$ t=0^+ \$ the instant the swich has been closed? \$\endgroup\$

Commented Apr 4, 2019 at 15:16

\$\begingroup\$ @Unknown123 Yes, of course. But the question asks for voltages and currents of the R's and the C, which, with switch open and C uncharged, you don't have to "calculate" for because it's (obviously?) 0. \$\endgroup\$

Commented Apr 5, 2019 at 10:15

2 Answers 2

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At t=0 , the capacitor is completely discharged and has 0V across it.

At t=infinity , the capacitor is fully charged. How much current will flow into/through the capacitor then? What voltage drop will occur due to that current across the 3.3k resistor?

Look at the charge curve of a capacitor, e.g. here:

It also has the values for t=0 and t->infinity .

You can see that for long t the charge and the voltage approach 100% while the current goes towards 0. Theoretically, the capacitor will only ever be exactly 100% charged after an infinite amount of time, but it will be very close to 100% (99.9999. %) after a small multiple of the R*C time constant. This can be seen from the 1-exp(-t/. ) term, which approaches 1 (100%) exponentially over t .