A parallel plate condenser has a uniform electric field \(E\)(V/m) in the space between the plates. If the distance between the plates is \(d\)(m) and area of each plate is \(A(\text{m}^2)\), the energy (joule) stored in the condenser is:
1. | \(\dfrac{1}{2}\varepsilon_0 E^2\) | 2. | \(\varepsilon_0 EAd\) |
3. | \(\dfrac{1}{2}\varepsilon_0 E^2Ad\) | 4. | \(\dfrac{E^2Ad}{\varepsilon_0}\) |
An electric dipole of moment \(\vec {p} \) is lying along a uniform electric field \(\vec{E}.\) The work done in rotating the dipole by \(90^{\circ}\) is:
1. \(\sqrt{2}pE\)
2. \(\dfrac{pE}{2}\)
3. \(2pE\)
4. \(pE\)
If \(V=ar\) where \(a\) is a constant and \(r\) is the distance, then the electric field at a point will be proportional to:
1. \(r\)
2. \(r^{-1}\)
3. \(r^{-2}\)
4. \(r^{0}\)
The charge on the plates of the capacitor in a steady-state will be:
1. \(3~\mu\text{C}\)
2. \(9~\mu\text{C}\)
3. \(27~\mu\text{C}\)
4. \(36~\mu\text{C}\)
Two identical capacitors \(C_{1}\) and \(C_{2}\) of equal capacitance are connected as shown in the circuit. Terminals \(a\) and \(b\) of the key \(k\) are connected to charge capacitor \(C_{1}\) using a battery of emf \(V\) volt. Now disconnecting \(a\) and \(b\) terminals, terminals \(b\) and \(c\) are connected. Due to this, what will be the percentage loss of energy?
1. | \(75\%\) | 2. | \(0\%\) |
3. | \(50\%\) | 4. | \(25\%\) |
Three identical capacitors are connected as follows:
Which of the following shows the order of increasing capacitance (smallest first)?
1. | \(\mathrm{(3), (2), (1)}\) | 2. | \(\mathrm{(1), (2), (3)}\) |
3. | \(\mathrm{(2), (1), (3)}\) | 4. | \(\mathrm{(2), (3), (1)}\) |
Two capacitors of capacitance \(6~\mu\text{F}\) and \(3~\mu\text{F}\) are connected in series with battery of \(30~\text{V}\). The charge on \(3~\mu\text{F}\) capacitor is:
1. \( 3 ~\mu\text{C}\)
2. \( 1.5 ~\mu\text{C}\)
3. \( 60~\mu\text{C}\)
4. \( 900~\mu\text{C}\)
The graph of electric potential \((V)\) versus distance \((r)\) is shown in the diagram. The value of the electric field at a distance \(A\) will be:
1. | \(5\) V/m | 2. | \(-10\) V/m |
3. | \(-5\) V/m | 4. | \(10\) V/m |
The equivalent capacitance of the given circuit is:
1. \(\dfrac{C}{2}\)
2. \(C\)
3. \(2C\)
4. \(4C\)