A $4\ \mu F$ capacitor, a resistance of $2.5 \,MW$$\Omega$ is in series with $12\, V$ battery. Find the time after which the potential difference across the capacitor is $3$ times the potential difference across the resistor.......$s$ [Given $ln(2)= 0.693$]
IIT 2005, Diffcult
Download our app for free and get started
(a) ${V_R} = \frac{{{V_0}}}{4}$
$=$ ${V_0}{e^{ - \frac{t}{{RC}}}}$
$==>$ $\frac{1}{4}$ $=$ ${e^{ - \frac{t}{{10}}}}$
$==>$ $4 = {e^{\frac{t}{{10}}}}$
$==>$ ${\log _e}4 = \frac{t}{{10}}$
$==>$ $t = 10\log 4 = 13.86 \,s$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1A non-conducting ring of radius $0.5\,m$ carries a total charge of $1.11 \times {10^{ - 10}}\,C$ distributed non-uniformly on its circumference producing an electric field $\vec E$ everywhere in space. The value of the line integral $\int_{l = \infty }^{l = 0} {\, - \overrightarrow E .\overrightarrow {dl} } \,(l = 0$ being centre of the ring) in volt isView Solution
- 2Three capacitors are connected as shown in fig. Then the charge on capacitor $C_1$ is.....$\mu C$View Solution
- 3In the circuit shown in figure, four capacitors are connected to a battery. The potential difference across the $6$ $\mu F$ capacitor is......$V$View Solution
- 4In the following diagram the work done in moving a point charge from point $P$ to point $A, B$ and $C$ is respectively as $W_A,\, W_B$ and $W_C$, then (there is no charge nearby)View Solution
- 5A $700\,pF$ capacitor is charged by a $50\,V$ battery. The electrostatic energy stored by it isView Solution
- 6Figure shows a solid hemisphere with a charge of $5\ nC$ distributed uniformly through its volume. The hemisphere lies on a plane and point $P$ is located on this plane, along a radial line from the centre of curvature at distance $15\ cm$. The electric potential at point $P$ due to the hemisphere, is .....$V$View Solution
- 7The capacitance of a parallel plate capacitor is $C$ when the region between the plate has air. This region is now filled with a dielectric slab of dielectric constant $k$. The capacitor is connected to a cell of $emf$ $E$, and the slab is taken outView Solution
- 8$512$ identical drops of mercury are charged to a potential of $2\, V$ each. The drops are joined to form a single drop. The potential of this drop is ......... $V.$View Solution
- 9View SolutionInside a hollow charged spherical conductor, the potential
- 10Six point charges are placed at the vertices of a regular hexagon of side $a$ as shown. If $E$ represents electric field and $V$ represents electric potential at $O$, thenView Solution
