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In the following circuit, the switch $S$ is closed at $t = 0.$ The charge on the capacitor $C_1$ as a function of time will be given by $\left( {{C_{eq}}\, = {\kern 1pt} \,\frac{{{C_1}{C_2}}}{{{C_1} + {C_2}}}} \right).$
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 $ln(2)= 0.693$]
Two identical capacitors $1$ and $2$ are connected in series. The capacitor $2$ contains a dielectric slab of constant $K$ as shown. They are connected to a battery of emf $V_0\ volts$ . The dielectric slab is then removed. Let $Q_1$ and $Q_2$ be the charge stored in the capacitors before removing the slab and $Q'_1$ , and $Q'_2$ be the values after removing the slab. Then
Two parallel plate condensers of capacity of $20 \mu F$ and $30 \mu F$ are charged to the potentials of $30V$ and $20V$ respectively. If likely charged plates are connected together then the common potential difference will be :-......$V$
A parallel plate capacitor has a uniform electric field ' $\overrightarrow{\mathrm{E}}$ ' in the space between the plates. If the distance between the plates is ' $\mathrm{d}$ ' and the area of each plate is ' $A$ ', the energy stored in the capacitor is : $\left(\varepsilon_{0}=\right.$ permittivity of free space)
A network of four capacitors of capacity equal to $C_1 = C, C_2 = 2C, C_3 = 3C$ and $C_4 = 4C$ are conducted in a battery as shown in the figure. The ratio of the charges on $C_2$ and $C_4$ is
A conducting body $1$ has some initial charge $Q$, and its capacitance is $C$. There are two other conducting bodies, $2$ and $3$, having capacitances : $C_2 = 2C$ and $C_3 \rightarrow \infty$ . Bodies $2 $ and $3 $ are initially uncharged. "Body $2$ is touched with body $1$. Then, body $2$ is removed from body $1 $ and touched with body $3$, and then removed." This process is repeated $N$ times. Then, the charge on body $1$ at the end must be
The capacitor $'C'$ is initially uncharged. Switch $S_1$ is closed for a long time while $S_2$ remains open. Now at $t = 0$ , $S_2$ is closed while $S_ 1$ is opened. All the batteries are ideal and connecting wires are resistanceless. Find $INCORRECT$ statement
A resistor '$R$' and $2\ μF$ capacitor in series is connected through a switch to $200\ V$ direct supply. Across the capacitor is a neon bulb that lights up at $120\ V$. Calculate the value of $R$ to make the bulb light up $5\ s$ after the switch has been closed. $(log_{10} 2.5 = 0.4)$.