Home
Class 12
PHYSICS
Obtain an expression for equivalent capa...

Obtain an expression for equivalent capacitance when three capacitors `C_1, C_2 and C_3` are connected in series.

Text Solution

Verified by Experts

Let three capacitors `C_(1),C_(2)` and `C_(3)` are connected in series. We know charge remains same in series combination.

`V_(1)=(q)/(C_(1))`
`V_(2)=(q)/(C_(2))`
`V_(3)=(q)/(C_(3))`
`V=V_(1)+V_(2)+V_(3)`
`=q((1)/(C_(1))+(1)/(C_(2))+(1)/(C_(3)))`
If the 3 capacitors are replaced by a single capacitor such that on giving it charge q, a capacitance C is obtained then `V=(q)/(C)`
`:.(q)/(C)=q((1)/(C_(1))+(1)/(C_(2))+(1)/(C_(3)))`
or `(1)/(C)=(1)/(C_(1))+(1)/(C_(2))+(1)/(C_(3))`
Promotional Banner

Similar Questions

Explore conceptually related problems

Deduce an expression for equivalent capacitance C when three capacitors C_(1), C_(2) and C_(3) are connected in parallel.

Obtain an expression for effective capacitance of two capacitors in series.

(b) Obtain the expression for the capacitance of a parallel plate capacitor.

The equivalent capacitance of three capacitors of capacitance C_(1):C_(2) and C_(3) are connected in parallel is 12 units and product C_(1).C_(2).C_(3) = 48 . When the capacitors C_(1) and C_(2) are connected in parallel, the equivalent capacitance is 6 units. then the capacitance are

Three capacitors each of capacitance C are connected in series. Their equivalent capacitance is C_(s) . The same three capacitors are now connected in parallel. Their equivalent capacitance becomes C_(p) . Find the ratio ((C_(p))/(C_(s))) (Working must be shown).

Find the equivalent capacitance between A and B. All the capacitors have capacitance C.

Find the equivalent capacitance between A and B. All the capacitors have capacitance C.

Four capacitors of equal capacitance have an equivalent capacitance C_(1) when connected in series and an equivalent capacitance C_(2) when connected in parallel. The ratio (C_(1))/(C_(2)) is

There are 7 identical capacitors. The equivalent capacitance when they are connected in series is C. The equivalent capacitance when they are connected in parallel is

The capacities of three capacitors are in ratio 1:2:3. Their equivalent capacity when connected in parallel is (60)/11 muF more than that when they are connected in series. The individual capacitors are of capacities in muF .