Question

Define a capacitor.
Draw a circuit diagram and obtain a relation for equivalent capacitance in the series combination of capacitors.
In given circuit diagram write the value of $V_1$.

Answer 1

Capacitor is an electrical system capable of storing electrical charge (electrical energy). It comprises of a single or two conductors carrying equal and opposite charge and separated by a potential. Its SI unit is farad ($F$). It is defined as the ratio of charge stored to the potential difference between the conductors.

$C=\frac{Q}{V}$

Consider the circuit shown in the attached figure with two capacitors in series.

In series, charge across the capacitors is same. Also, the charge across the equivalent capacitor is also the same.

$Q_1=Q_2=Q..........\left(i\right)$

Using KVL, $V=V_1+V_2.............\left(ii\right)$

Using definition of capacitance,

$C_{eq}=QV..........\left(iii\right)$

$C_1=Q{V}_1..........\left(iv\right)$

$C_2=Q{V}_2...........\left(v\right)$

Substituting (iii), (iv) and (v) in (ii), we get

$\frac{Q}{C_{eq}}=\frac{Q}{C_1}+\frac{Q}{C_2}$

$\frac{1}{C_{eq}}=\frac{1}{C_1}+\frac{1}{C_2}$

Now, consider the circuit in the attached figure.

Using KVL, $V=V_1+V_2$

$10=V_1+4$

$V_1=6V$