\n A capacitor is a device that stores energy in the form of an electric field. It comprises of two conducting plates\r\n carrying equal and opposite charges and separated by an insulating medium.\r\n The magnitude of the electric charge \\(Q\\) stored in the capacitor is proportional to the voltage difference \\(V\\) between the two conducting plates, i.e.,\r\n $$Q \\propto V$$\r\n The proportionality constant is known as capacitance of the capacitor, and is denoted by \\(C\\).\n
\r\n $$Q=CV$$\r\n\n When two or more capacitors are connected in such a way that plates of adjacent capacitors are connected\r\n with each other i.e., only the first plate of first capacitor and second plate of the last capacitor is connected\r\n to the source, the combination is known as series.
In series combination the magnitude of charge on each\r\n capacitor is same. Consider \\(n\\) capacitors (\\(C_1\\),\\(C_2\\), … , \\(C_n\\) ) connected in series.\n
Because they are connected in series, all the capacitors carry same amount of electric charge.
\r\n $$Q=C_1V_1 = C_2 V_2 = .... = C_n V_n$$\r\n where \\(V_n\\) is the voltage difference across \\(n^{th}\\) capacitor.\r\n\n Voltage difference across \\(n^{th}\\) capacitor is given as:\r\n $$V_n = Q/C_n$$\r\n Total voltage difference is the sum of voltage differences across individual capacitors, i.e.,\n
\r\n $$V=V_1+V_2+...+V_n$$\r\nThe equivalent capacitance C is given by:
\r\n $$\\frac{1}{C_{eq}} = \\frac{1}{C_1} + \\frac{1}{C_2} +...+ \\frac{1}{C_n}$$\n\n When two or more capacitors are connected in such a way that one plate of all the capacitors are\r\n connected to one point of the source and other plate of all the capacitors are connected to other single\r\n point of the source, the combination is known as parallel combination. In parallel combination, potential\r\n difference \\(V\\) is same across all the capacitors. Now consider \\(n\\) capacitors \\(C_1\\), \\(C_2\\), … , \\(C_n\\) connected in parallel. For such capacitors:\r\n
\r\n\n Charge on each capacitor (say \\(Q_i\\)) is different and is given as:\r\n $$Q_i = C_i V$$.\r\n
Total charge \\(Q\\) is the sum of individual charges on each capacitor and is given as:\n
The potential difference across each capacitor is same as the source i.e.,
\r\n $$V_i=\\frac{Q_i}{C_i}=V$$\r\nThe equivalent capacitance \\(C_{eq}\\) is given by:
\r\n $$C_{eq}=C_1 + C_2 + ...+ C_n$$\r\n