Answer:
U= 1.9*10^-7
Explanation:
given:
L=8 cm
d_1=d_2=2.05_10^-3
K_py=4.3
K_po=3
V_ab=86 V
required
U=??
solution:
the energy stored in the capacitor
U=1/2C_t*V^2_ab (1)
voltage is known but capacitance is not
we can consider the two plates of polystyrene and pyrex glass as a two separate capacitors connected on series so the total capacitance of series capacitor is given by:
1/C_t= 1/C_py+1/C_po (2)
the capacitance of polystyrene
C_po=K_po*A/d
=8.9*10^-11
= 89 pF
the capacitance of pyrex
C_py=K_py*A/d
=128 pF
substitution in 2 yields
1/C_t= 1/128+1/89
C_t= 52.6 pF
substitution in 1 yields
U=1/2C_t*V^2_ab
= 1.9*10^-7
Answer:
2.29 x 10^-7 J.
Explanation:
Hiven:
L = 9 cm
= 0.09 m
d = 2.05 mm
= 2.05 x 10^-3 m
ε° * kpo = 2.56 * 8.854 x 10^-12
= 2.27 x 10-11
ε° * kpo = 5.6 * 8.854 x 10^-12
= 5 x 10-11
V = 86 V
The two plates of polystyrene and pyrex glass as a two separate capacitors connected on series so the total capacitance of series capacitor is given by:
1/CT = 1/Cpy + 1/Cpo
Capacitance of polystyrene, Cpo = ε° * kpo * A/d
Area = L^2
= 0.09^2
= 0.0081 m^2
d = 0.00205 m
Cpo = 2.27 x 10^-11 * 0.0081/0.00205
= 9 x 10^-11 F
Capacitance of pyrex, Cpy = ε° * kpy * A/d
= 5 x 10^-11 * 0.0081/0.00205
= 2 x 10^-10 F
1/CT = 1/9 x 10^-11 + 1/2 x 10^-10
CT = 6.19 x 10^-11 F
Energy stored in the capacitor
U = 1/2 * C * V^2
= 1/2 * 6.19 x 10^-11 * 86^2
= 2.29 x 10^-7 J.
