1. The capacitance of a capacitor is NOT influenced by:
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The geometric formula for a parallel-plate capacitor is $C = \frac{\varepsilon_r \varepsilon_0 A}{d}$. Capacitance depends solely on the overlapping surface area of the plates ($A$), the separation distance ($d$), and the dielectric material ($\varepsilon_r$). The physical thickness of the conducting plates plays no role in holding electric fields.
2. What is the value of capacitance of a capacitor which has a voltage of 4V and has 16C of charge?
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Using the standard charge relationship formula $Q = CV$, we can rearrange it to isolate capacitance: $C = \frac{Q}{V}$. Substituting the given values: $C = \frac{16\text{ C}}{4\text{ V}} = 4\text{ Farads (F)}$.
3. Capacitors are used in electric power supply systems to:
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Industrial electrical grids typically drive heavy inductive loads (like motors and transformers) which cause the current to lag behind the voltage, lowering the power factor. Shunt capacitor banks supply localized reactive power, neutralizing this lagging inductive phase shift and **improving the system's power factor**. While improving the power factor does secondary things like reducing line current, its *primary, designated system purpose* is power factor correction.
4. In a variable capacitor, capacitance can be varied by:
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Standard variable tuning capacitors (like those used in old radio tuners) feature a set of fixed stator plates and a set of movable rotor plates attached to a central shaft. Rotating the shaft swings the moving plates in or out of alignment, changing the effective **overlapping surface area ($A$)**, which directly scales the net capacitance.
5. Energy stored in the capacitor is:
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The electrostatic potential energy $E$ packed into a capacitor's field is calculated by integrating the work required to move incremental charges against increasing voltage: $E = \int V \, dq = \int \frac{q}{C} \, dq = \frac{1}{2}\frac{Q^2}{C} = \frac{1}{2}CV^2$.
6. The time constant of a series RC circuit consisting of a $100\mu\text{F}$ capacitor in series with a $100\,\Omega$ resistor is:
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The capacitive time constant is $\tau = RC$. Given $R = 100\,\Omega$ and $C = 100\mu\text{F} = 100 \times 10^{-6}\text{ F}$: $$\tau = 100 \times (100 \times 10^{-6}) = 10^4 \times 10^{-6} = 10^{-2}\text{ s} = 0.01\text{ s}.$$
*(Note: While option (c) evaluates directly to the correct mathematical calculation of $0.01\text{ s}$, standard answer keys for this specific regional board question typically print a typo in the original question where the resistor is meant to be $1000\,\Omega$ to match option (a) $0.1\text{ s}$. Under a strict interpretation of your provided numbers, $100\,\Omega \times 100\mu\text{F}$ equals exactly **$0.01\text{ s}$ (option c)**).*
7. The charging of a capacitor through a resistance follows:
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Solving the differential equation derived from Kirchhoff's Loop Rule for a series RC network yields the transient charge formula: $q(t) = Q_0(1 - e^{-t/RC})$. This confirms that transient charging profiles follow an **exponential law**.
8. When the total charge in a capacitor is doubled, the energy stored:
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Expressed in terms of net charge, stored electrostatic energy is $E = \frac{Q^2}{2C}$. Because energy scales quadratically with charge ($E \propto Q^2$), doubling the accumulated charge cargo ($2Q$) scales the overall potential energy output by a factor of four ($2^2 = 4$), **quadrupling** it.
9. The capacitance C is charged through a resistor R. The time constant of the charging circuit is given by:
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By definition, the scaling factor governing transient rates inside capacitive loops is the product of ohmic resistance and faradic capacitance: $\tau = RC$. One time constant represents the duration required for a charging empty capacitor to reach approximately $63.2\%$ of its maximum theoretical capacity.
10. A capacitor blocks:
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The capacitive reactance expression is $X_C = \frac{1}{2\pi f C}$. For steady-state direct current (DC), the source frequency is zero ($f = 0$), driving the capacitive impedance toward infinity ($X_C \to \infty$). Thus, **a capacitor completely blocks DC** while permitting time-varying alternating current (AC) signals to pass through via displacement current.
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