If two capacitors are wired in series and C1 = 4 μ F and C2 = 12 μ F, what is the equivalent cap

Step 1: Recall the formula for calculating the equivalent capacitance of capacitors wired in ser

If two capacitors are wired in series and C1 = 4 μ F and C2...

If two capacitors are wired in series and $C_1 = 4 \mu F$ and $C_2 = 12 \mu F$, what is the equivalent capacitance of the circuit? $4 \mu F$ $16 \mu F$ $3 \mu F$ $12 \mu F$ $0 \mu F$

Transcript

00:01 Hi there.

00:02 So for this problem, we have two capacitors give an equivalent capacitance of cp when they are in a parallel configuration and cs when they are in series.

00:22 Now, with that said, the question is, what is the capacitance of each capacitor for this? because remember that we have two capacitors in this for this problem.

00:33 So let me start by writing the expression.

00:38 So we know that when we have two capacitors in parallel, the equivalent capacitance is just equal to the sum of the capacitance 1 plus the capacitance 2.

00:50 And for in series, we have that 1 divided by the capacitance in series is equal to the inverse.

00:59 The sum of inverse of the capacitors, in this case, capacitor 1 and the capacitor 2.

01:05 Now, what we are going to do is to solve for the capacitance 2 from the first expression.

01:14 So we obtain this, and then we can substitute this into the capacitance in series.

01:22 So we will obtain 1 divided by the capacitance in series is equal to 1 divided by the capacitance 1.

01:29 This plus 1 divided by the capacitance in parallel minus the capacitance 1.

01:36 Now, we expand this in here.

01:40 We will obtain that the inverse of the capacitance in series is equal to the capacitance in parallel minus the capacitance 1 plus the capacitance 1, and this divided by c1 times cp8 minus c1.

01:56 Now, simplifying this, we will obtain from this equation.

02:00 C1 to the square minus c1 times cp plus cp times cs.

02:07 And then this is equal to zero.

02:10 So what we can do in this case is to use the quadratic...

Question

If two capacitors are wired in series and $C_1 = 4 \mu F$ and $C_2 = 12 \mu F$, what is the equivalent capacitance of the circuit? $4 \mu F$ $16 \mu F$ $3 \mu F$ $12 \mu F$ $0 \mu F$

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