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Two capacitors of $2$ $\mu F$ and $3$ $\mu F$ are charged to $150$ $volt$ and $120$ $volt$ respectively. The plates of capacitor are connected as shown in the figure. A discharged capacitor of capacity $1.5$ $\mu F$ falls to the free ends of the wire. Then
The diagram below shows electric field lines in a region of space. Which of the following diagrams best shows the variation with distance $d$ of the potential $V$ along the line $XY$ as we move from $X$ to $Y$ ?
Voltage rating of a parallel plate capacitor is $500\,V$. Its dielectric can withstand a maximum electric field of ${10^6}\,\frac{V}{m}$. The plate area is $10^{-4}\, m^2$ . What is the dielectric constant if the capacitance is $15\, pF$ ? (given ${ \in _0} = 8.86 \times {10^{ - 12}}\,{C^2}\,/N{m^2}$)
If $50$ joule of work must be done to move an electric charge of $2 \,C$ from a point, where potential is $-10$ volt to another point, where potential is $V$ volt, the value of $V$ is ......... $V$
A charge of $10 \,\mu C$ is placed at the origin of $x-y$ coordinate system. The potential difference between two points $(0, a)$ and $(a, 0)$ in volt will be
A parallel plate capacitor has a uniform electric field $E$ in the space between the plates. If the distance between the plates is $d$ and area of each plate is $A,$ the energy stored in the capacitor is
The plates of a capacitor are charged to a potential difference of $320 \, volts$ and are then connected across a resistor. The potential difference across the capacitor decays exponentially with time. After $1 $ second the potential difference between the plates of the capacitor is $240 \, volts$, then after $2$ and $3$ seconds the potential difference between the plates will be
A parallel plate capacitor is made of two square parallel plates of area $A$ , and separated by a distance $d < < \sqrt A $ . The capacitor is connected to a battery with potential $V$ and allowed to fully charge. The battery is then disconnected. A square metal conducting slab also with area $A$ but thickness $\frac {d}{2}$ is then fully inserted between the plates, so that it is always parallel to the plates. How much work has been done on the metal slab by external agent while it is being inserted?