a simple rc circuit of a 1uf capacitor in series with 2800 ohm resistor a 60v battery and an ope

Step 1: The formula for the voltage across the capacitor as a function of time is given by ( V(

A simple rc circuit of a 1uf capacitor in series with 2800...

A simple RC circuit consists of a 1uF capacitor in series with a 2800 ohm resistor, a 6.0V battery, and an open switch. Initially, the capacitor is uncharged. Calculate how long after the switch is closed will the voltage across the capacitor be 4.1V.

Transcript

00:01 So in this question we are given there is an rc circuit basically.

00:06 So this is r, this is c and charging is happening basically here.

00:15 So voltage v.

00:16 So when you close this, what will happen? the charge on this capacitor will slowly rise and hence the potential will also rise.

00:24 So the variation of charge with the passage of time is given as q is equal to cb in to 1 minus e -rest to the power minus t upon rc so this is the variation of charge which is a very standard formula this is known to us and now what we need to do is we need to find the potential on the capacitor also right so charge in a capacitor is known to us we know that q is equal to cb right so now the potential on the capacitor would be equal to q by c so potential on the i'm calling this v -dash as a potential on the capacitor which would be equal to q by c so the value of q is here so we can write it c v into 1 minus series to power minus t by rc this is q divided by c so v -dash is coming out to be v -dash is the voltage across the capacitor as a function of time so this value is coming out to be v which is battery potential into 1.

01:32 1 minus a to power minus t by rc.

01:37 So now we are also given certain data.

01:40 The data which is given to us, i'm writing it here.

01:43 We are given the value of resistance, which is 280 .0.

01:48 We are given the value of capacitor, which is one microperid, which means 10 to power minus of 6 ferret.

01:55 Okay, we are given the voltage, which we are applying this voltage battery.

02:01 It is given as 6 bolt and we need to find the time at which the time at which the potential v prime will become equal to 4 .1 so now so from here we are putting here b prime is equal to 4 .1 which is equal to v battery potential which is given to us 6 volt 6 into 1 minus e to the power minus t and then divided by rc.

02:33 The value of r is 2 ,800...

Question

A simple RC circuit consists of a 1uF capacitor in series with a 2800 ohm resistor, a 6.0V battery, and an open switch. Initially, the capacitor is uncharged. Calculate how long after the switch is closed will the voltage across the capacitor be 4.1V.

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