Derive an expression for effective capacitance of three capacitorsconnected in parallel.An electric dipole consists of two opposite charges each ofmagnitude 1μC separated by 2cm. The dipole is placed in anexternal electric field of 10 ^ 5 * N / C . Calculate the maximum torqueexerted by the field on the dipole.
Answers
Given:- An electric dipole consist at two opposite charge each of magnitude = =1μC=1×10−6C
distance =2cm Exter field =10 5 N/C
To find:- Maximum torque
Solution:-
q=1×10 −6 C,2a=2cm or, =0.02cm
∴ P=q×2a =(1×10^−6 )×0.02 =2×10^−8 cm
Intensity of the external electric field, E=1.0×10 5 N/C
(i) Z max =pE=(2×10^−8 )*(10×10^5 )=2×10^−3 N−m
(ii) Net work done in turning the dipole from 0 to 180 degrees i.e
W=∫rdθ=∫pEsinθdθ Use upper limit as 180 and lower limit as 0
= pE[−cosθ]
= −pE(cos180−cos0)
=2pE
=2×(2×10−8)(1×105)J
=4×10−3J
Expression for effective capacitance of three capacitors in parallel is given as
capacitors C 1 ,C 2 andC 3 are connected in parallel.
The same potential is applied across all the three capacitors.
Let Q 1 ,Q 2 andQ 3 are charges on the three plates of capacitors such that Q 1 =C 1 *V
Q 2 =C 2 *V
Q 3 =C 3 *V
The total charge stored is Q=Q 1 +Q 2 +Q 3 and equivalent capacitance is C eq = Q/V
So, C eq = (Q 1 +Q 2 +Q 3)/V = Q 1/V + Q 2/V + Q 3/V
C eq =C 1 +C 2 +C 3