Advertisements
Advertisements
Question
Calculate the resultant capacitances for each of the following combinations of capacitors.
Advertisements
Solution
Parallel combination of capacitor 1 and 2
Cp = C0 + C0 = 2C0
Series combination of capacitor Cp and 3
`1/"C"_"s" = 1/"C"_"p" + 1/"C"_3 = 1/(2 "C"_0) + 1/"C"_0 = ("or") 1/"C"_"s" = 3/2 "C"_0 ("or") "C"_"s" = 2/3 "C"_0`
`1/"C"_("s"_1) = 1/"C"_1 + 1/"C"_2 = 1/"C"_0 + 1/"C"_0 = 1/"C"_0` (or)
`1/"C"_("s"_1) = 2/"C"_0 ("or") "C"_("S"_1) = "C"_0/2`
Similarly 3 and 4 are series combination
`1/"C"_("s"_1) = 1/"C"_3 + 1/"C"_4 = 1/"C"_0 + 1/"C"_0 = 2/"C"_0 ("or") "C"_("S"_2) = "C"_0/2`
`"C"_("S"_1) and "C"_("S"_2)` are in parallel combination
`"C"_"p" = "C"_("S"_1) + "C"_("S"_2) = "C"_0/2 + "C"_0/2 ("or") "C"_"p" = (2"C"_0)/2 "C"_"p" = "C"_0`- Capacitor 1, 2 and 3 are in parallel combination
Cp = C0 + C0 + C0 = 3C0
Cp = 3C0
- Capacitar C1 and C2 are in combination
`1/"C"_("s"_1) = ("C"_1 + "C"_2)/("C"_1"C"_2)`
`"C"_("s"_1) = ("C"_1"C"_2)/("C"_1 + "C"_2)`
Similarly C3 and C4 are in series combination
`1/"C"_("s"_2) = 1/"C"_3 + 1/"C"_4 = ("C"_3 + "C"_4)/("C"_3"C"_4)`
`"C"_("s"_2) = ("C"_3"C"_4)/("C"_3 + "C"_4)`
`"C"_("s"_1) and "C"_("s"_2)` are in parallel combination across RS:
CP = `"C"_("S"_1) + "C"_("S"_2)`
`= ("C"_1"C"_2)/("C"_1 + "C"_2) + ("C"_3"C"_4)/("C"_3 + "C"_4)`
`= ("C"_1"C"_2 ("C"_3 + "C"_4) + "C"_3"C"_4("C"_1 + "C"_2))/(("C"_1 + "C"_2)("C"_3 + "C"_4))`
`"C"_"P" = ("C"_1"C"_2"C"_3 + "C"_1"C"_2"C"_4 + "C"_3"C"_4"C"_1 + "C"_3"C"_4"C"_2)/(("C"_1 + "C"_2)("C"_3 + "C"_4))` - Capacitor 1 and 2 are series combination
`1/"C"_("s"_1) = 1/"C"_1 + 1/"C"_2 = 1/"C"_0 + 1/"C"_0 = 1/"C"_0`
`1/"C"_("s"_1) = 2/"C"_0` (or) `"C"_"s"_1 = "C"_0/2`
Similarly 3 and 4 are series combination
`1/"C"_("s"_1) = 2/"C"_0 ("or") "C"_("s"_2) = "C"_0/2`
Three capacitors are in parallel combination
`"C"_"P" = "C"_0/2 + "C"_0 + "C"_0/2 + (2"C"_0)/2 + "C"_0/2 = (4"C"_0)/2`
`"C"_"P" = 2 "C"_0`
APPEARS IN
RELATED QUESTIONS
Define capacitor reactance. Write its S.I units.
A capacitor of unknown capacitance is connected across a battery of V volts. The charge stored in it is 300 μC. When potential across the capacitor is reduced by 100 V, the charge stored in it becomes 100 μC. Calculate The potential V and the unknown capacitance. What will be the charge stored in the capacitor if the voltage applied had increased by 100 V?
A capacitor is formed by two square metal-plates of edge a, separated by a distance d. Dielectrics of dielectric constant K1 and K2 are filled in the gap as shown in figure . Find the capacitance.
A parallel-plate capacitor of plate area A and plate separation d is charged to a potential difference V and then the battery is disconnected. A slab of dielectric constant K is then inserted between the plates of the capacitor so as to fill the space between the plates. Find the work done on the system in the process of inserting the slab.
Consider an assembly of three conducting concentric spherical shell of radii a, b and c as shown in figure Find the capacitance of the assembly between the points Aand B.
Three circuits, each consisting of a switch 'S' and two capacitors, are initially charged, as shown in the figure. After the switch has been closed, in which circuit will the charge on the left-hand capacitor
(i) increase,
(ii) decrease, and
(iii) remains the same? Give reasons.
Two plates A and B of a parallel plate capacitor are arranged in such a way, that the area of each plate is S = 5 × 10-3 m 2 and distance between them is d = 8.85 mm. Plate A has a positive charge q1 = 10-10 C and Plate B has charge q2 = + 2 × 10-10 C. Then the charge induced on the plate B due to the plate A be - (....... × 10-11 )C
A capacitor has charge 50 µC. When the gap between the plate is filled with glass wool, then 120 µC charge flows through the battery to capacitor. The dielectric constant of glass wool is ______.
Current versus time and voltage versus time graphs of a circuit element are shown in figure.
 |
 |
The type of the circuit element is ______.
