Advertisements
Advertisements
Question
Find the equivalent capacitances of the combinations shown in figure between the indicated points.
Advertisements
Solution
Applying star-delta conversion in the part indicated in the diagram.
The Capacitance of the `C_1` is given by
`C_1^' = (C_2C_3)/(C_1+C_2+C_3)`
`C_2^' = (C_1C_3)/(C_1+C_2+C_3)`
`C_3^' = (C_1C_2)/(C_1+C_2+C_3)`
⇒ `C_1'^ = (3 xx 4)/(1+3+4) = 12/8 "uF"`
⇒ `C_2^' = (1 xx 3)/(1+3+4) = 3/8 "uF"`
⇒ `C_3^' = (1 xx 4)/(1+3+4) = 4/8 "uF"`
Thus, the equivalent circuit can be drawn as :
Therefore, the equivalent capacitance is given by
`C_(eq) = 3/8 + [((3+1/2) xx (3/2+1))/((3+1/2)+(3/2+1))]` = `3/8 + 35/24 = (9+35)/24 = 11/6 "uF"`
`1+1 = 2 "uF"`
(c)
It is a balanced bridge.
Therefore, the capacitor of capacitance 5 μF can be removed.
Cef = `4/3+8/3+4 = 8 "uF"`
The capacitance of the two branches are :
`C_1 = (2 xx 4)/(2+4) = 4/3 uF`
`C_2 = (4 xx 8)/(4+8) = 8/3 uF`
∴ Equivalent capacitance = `4/3 + 8/3 + 4 = 8 "uF"`
It can be observed that the bridges are balanced.
Therefore, the capacitors of capacitance 6 μF between the branches can be removed
The capacitances of the four branches are :
`C_1 = (2 xx 4)/(2+4) = 4/3 uF`
`C_2 = (4 xx 8)/(4+8) = 8/3 uF`
`C_3 = (4 xx 8)/(4+8) = 8/3 uF`
`C_4 = (2 xx 4)/(2+4) = 4/3 uF`
∴ Equivalent capacitance
= `4/3 + 8/3 + 8/3 + 4/3`
= ` 8 "uF"`
APPEARS IN
RELATED QUESTIONS
A capacitor of capacitance ‘C’ is charged to ‘V’ volts by a battery. After some time the battery is disconnected and the distance between the plates is doubled. Now a slab of dielectric constant, 1 < k < 2, is introduced to fill the space between the plates. How will the following be affected? (b) The energy stored in the capacitor Justify your answer by writing the necessary expressions
Obtain the equivalent capacitance of the network in Figure. For a 300 V supply, determine the charge and voltage across each capacitor.
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?
Two capacitors each having capacitance C and breakdown voltage V are joined in series. The capacitance and the breakdown voltage of the combination will be
When 1⋅0 × 1012 electrons are transferred from one conductor to another, a potential difference of 10 V appears between the conductors. Calculate the capacitance of the two-conductor system.
The outer cylinders of two cylindrical capacitors of capacitance 2⋅2 µF each, are kept in contact and the inner cylinders are connected through a wire. A battery of emf 10 V is connected as shown in figure . Find the total charge supplied by the battery to the inner cylinders.
Each of the capacitors shown in figure has a capacitance of 2 µF. find the equivalent capacitance of the assembly between the points A and B. Suppose, a battery of emf 60 volts is connected between A and B. Find the potential difference appearing on the individual capacitors.
A capacitor is made of a flat plate of area A and a second plate having a stair-like structure as shown in figure . The width of each stair is a and the height is b. Find the capacitance of the assembly.
Each capacitor shown in figure has a capacitance of 5⋅0 µF. The emf of the battery is 50 V. How much charge will flow through AB if the switch S is closed?
Find the capacitances of the capacitors shown in figure . The plate area is Aand the separation between the plates is d. Different dielectric slabs in a particular part of the figure are of the same thickness and the entire gap between the plates is filled with the dielectric slabs.
If the voltage applied on a capacitor is increased from V to 2V, choose the correct conclusion.
Derive the expression for resultant capacitance, when the capacitor is connected in series.
The positive terminal of 12 V battery is connected to the ground. Then the negative terminal will be at ______.
The work done in placing a charge of 8 × 10–18 coulomb on a condenser of capacity 100 micro-farad is ______.
Three capacitors 2µF, 3µF, and 6µF are joined in series with each other. The equivalent capacitance is ____________.
The capacitance of a parallel plate capacitor is 60 µF. If the distance between the plates is tripled and area doubled then new capacitance will be ______.
The radius of a sphere of capacity 1 microfarad in the air is ______
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 ______.
The plates of a parallel plate capacitor are separated by d. Two slabs of different dielectric constant K1 and K2 with thickness `3/8 d and d/2`, respectively, are inserted in the capacitor. Due to this, the capacitance becomes two times larger than when there is nothing between the plates. If K1 = 1.25 K, the value of K1 is:
