In the given figure, the charge stored in \(6\mu F\) capacitor, when points A and B are joined by a connecting wire is _______\(\mu C\).
Correct Answer: 36
Solution and Explanation
Given: DC source of 9 V. A 6 Ω resistor is on the left vertical branch (top), a 3 Ω resistor on the right vertical branch (bottom). A 3 µF capacitor is at the left bottom to ground, and a 6 µF capacitor is on the right vertical branch. Points A and B are connected by a wire (so \(V_A=V_B\)).
Idea at steady state: For a DC source as \(t\to\infty\), capacitors behave as open circuits (no steady current through them). Thus only the resistors conduct.
1) Replace capacitors by opens and find the current path
Only the series path through the 6 Ω (left top) and 3 Ω (right bottom) resistors remains between the 9 V terminal and ground. Hence \[ R_{\text{eq}} = 6\,\Omega + 3\,\Omega = 9\,\Omega . \] Total current through the series branch: \[ i = \frac{V_{\text{source}}}{R_{\text{eq}}} = \frac{9}{9} = 1\ \text{A}. \]
2) Node voltages
Voltage drop across the 6 Ω resistor: \[ \Delta V_{6\Omega} = i \cdot 6 = 1 \times 6 = 6\ \text{V}. \] Let the top rail be \(9\ \text{V}\) and ground be \(0\ \text{V}\). The node between the 6 Ω and the (open) 3 µF (point \(A\)) is therefore \[ V_A = 9\ \text{V} - \Delta V_{6\Omega} = 9 - 6 = 3\ \text{V}. \] Since \(A\) and \(B\) are directly connected by a wire, \[ V_B = V_A = 3\ \text{V}. \]
3) Voltage across the 6 µF capacitor
The 6 µF capacitor is connected between the top rail (9 V) and node \(B\) (3 V). Hence \[ \Delta V_{6\mu\mathrm{F}} = 9\ \text{V} - 3\ \text{V} = 6\ \text{V}. \]
4) Charge on the 6 µF capacitor
\[ Q = C\,\Delta V = (6\,\mu\text{F}) \times (6\ \text{V}) = 36\,\mu\text{C}. \]
Result: The potential difference across the \(6\,\mu\text{F}\) capacitor is \(6\ \text{V}\) and the charge stored is \[ \boxed{Q = 36\,\mu\text{C}}. \]
Top JEE Main Physics Questions
- In a hydrogen like atom, when an electron jumps from the $M$ - shell to the $L$ - shell, the wavelength of emitted radiation is $\lambda$. If an electron jumps from $N$-shell to the $L$-shell, the wavelength of emitted radiation will be :
- Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:
A black body is at a temperature of 2880 K. The energy of radiation emitted by this body with wavelength between 499 nm and 500 nm is U1, between 999 nm and 1000 nm is U2 and between 1499 nm and 1500 nm is U3. The Wien's constant, b = 2.88×106 nm-K. Then,
- $I _{ CM }$ is the moment of inertia of a circular disc about an axis (CM) passing through its center and perpendicular to the plane of disc $I_{A B}$ is it's moment of inertia about an axis $AB$ perpendicular to plane and parallel to axis $CM$ at a distance $\frac{2}{3} R$ from center Where $R$ is the radius of the dise The ratio of $I _{ AB }$ and $I _{ CM }$ is $x: 9$ The value of $x$ is______
- A nucleus disintegrates into two smaller parts, which have their velocities in the ratio $3: 2$ The ratio of their nuclear sizes will be $\left(\frac{x}{3}\right)^{\frac{1}{3}}$ The value of ' $x$ ' is:-
Top JEE Main Capacitors in Parallel and in Series Questions
Top JEE Main Questions
- In a hydrogen like atom, when an electron jumps from the $M$ - shell to the $L$ - shell, the wavelength of emitted radiation is $\lambda$. If an electron jumps from $N$-shell to the $L$-shell, the wavelength of emitted radiation will be :
- Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:
What will be the equilibrium constant of the given reaction carried out in a \(5 \,L\) vessel and having equilibrium amounts of \(A_2\) and \(A\) as \(0.5\) mole and \(2 \times 10^{-6}\) mole respectively?
The reaction : \(A_2 \rightleftharpoons 2A\)- The value of is
- The number of terms of an is even. The sum of the odd terms is and of the even terms is . The last term exceeds the first by . Then the number of terms in the series is ______.