Find (a) the equivalent capacitance of the capacitors in Figure P 16.39,(b) the charge on each c

Find (a) the equivalent capacitance of the capacitors in...

Key Concepts

Potential Difference Across Capacitors

The potential difference, or voltage, across a capacitor is determined by the stored charge and its capacitance (V = Q/C). In analyzing circuits, especially when capacitors are connected in series, the total applied voltage is divided among the individual capacitors according to their capacitance values. In parallel configurations, all capacitors share the same voltage despite possibly storing different amounts of charge.

Series and Parallel Configurations

Understanding how capacitors are arranged—either in series or parallel—is essential because it affects the calculation of the equivalent capacitance, the distribution of charge, and the division of voltage across each component. This concept is fundamental in circuit analysis, as each configuration has a distinct method for combining individual capacitor values to analyze the overall circuit behavior.

Equivalent Capacitance

This concept refers to replacing a complex network of multiple capacitors with a single capacitor that has the same overall capacity to store charge. Depending on whether the capacitors are connected in series or parallel, different formulas are used. For series connections, the reciprocals of the capacitances add to give the reciprocal of the equivalent capacitance. For parallel connections, the capacitances add directly to give the equivalent capacitance.

Capacitor Charge Distribution

Charge distribution in capacitor circuits depends on the way the capacitors are connected. In a series circuit, each capacitor carries the same charge because the charge has only one path, whereas in a parallel circuit, the voltage across each capacitor is the same, but the charge stored on each capacitor is proportional to its capacitance.

Transcript

00:01 So here we have the circuit and these are the capacitors 8 microferret, 6 microferret, 2 microferret and 8 microferret connected here and we need to find out the total capacitance of this circuit.

00:15 So as these two capacitors are connected in parallel, so we will effectively use the expression for the capacitance is connected in parallel, it will be c1 plus c2.

00:26 And for the capacitance in series we use c1c2 by c1 plus c2.

00:33 So as these two capacitors are in parallel, so the net capacitance here will be 6 plus 2, that is 8 microferret.

00:44 And this 8 and this 8 and this 8, these three capacitors are now connected in series.

00:52 So the net capacitance will be now 1 by c1 plus 1 by c2 plus 1 by c2 plus 1 by c2.

01:00 3 is equal to 1 by c in series.

01:04 So here we put the values, we get 1 by c s as 1 by 8 plus 1 by 8 plus 1 by it so into 3 times.

01:11 So this gives us the capacitance as 8 by 3.

01:16 So this is the net capacitance of the given circuit here.

01:26 So this is the net capacitance.

01:29 And let us find out on each capacitor what will be the charge.

01:36 So, as we have figured out the net capacitance, the total voltage applied here is 9 volt.

01:43 Volt voltage sources 9 volt.

01:45 So we know that charge will be c into v.

01:50 This is the net charge which will be emitted from the battery.

01:54 It will be 8 by 3 into 9 that is 24 microculum because we have taken in microferret.

02:00 So this is the charge which is emitted by the battery, 24 microculum.

02:05 So, on this capacitor, the charge will be 24 microculum only.

02:13 So this plate will have plus 24, this will have minus 24.

02:16 Similarly this plate here will have minus 24 microculum and here we'll have plus 24 microculum charge and here the charge will be divided and in what ratio it will be divided.

02:31 Let us figure out that.

02:32 So basically 24 microculum charges coming out here...

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