Electrical Engineering All Engineering Career

The time constant (\( \tau \)) of an RC circuit is defined as the time during which the charging current falls to approximately 37% of its initial maximum value.

So, the correct option is:

37

In a capacitor, the electric charge is stored in the dielectric material as well as on the metal plates. When a capacitor is charged, electrons accumulate on one plate, creating a negative charge, while an equal and opposite positive charge accumulates on the other plate. The dielectric material between the plates enhances the capacitance by reducing the electric field strength between them, allowing more charge to be stored for a given voltage.

So, the correct option is:

dielectric as well as metal plates

Mica capacitors are commonly used for audio frequency and radio frequency coupling and tuning. Mica capacitors offer high stability, low loss, and good performance at high frequencies, making them suitable for such applications in electronic circuits.

So, the correct option is:

Mica

The power dissipated in a pure capacitor is zero. 

In an ideal capacitor, there is no resistance, so no power is dissipated as heat. The energy stored in the electric field between the plates is continuously exchanged between electric potential energy and kinetic energy of the charges as they move back and forth during charging and discharging cycles. However, there is no net energy loss.

So, the correct option is:

zero

Among the options provided, electrolytic capacitors generally have a relatively shorter shelf life compared to other types of capacitors such as mica, ceramic, or paper capacitors. Electrolytic capacitors rely on an electrolyte solution, which can degrade over time, leading to a decrease in performance and reliability. Additionally, electrolytic capacitors are prone to drying out if not used for an extended period, further reducing their shelf life.

So, the correct option is:

Electrolytic capacitor

Electric field intensity (\(E\)) is a vector quantity. 

A vector quantity is defined by both magnitude and direction. In the case of the electric field intensity, the magnitude represents the strength of the electric field, and the direction indicates the direction in which a positive test charge would move if placed in the field.

So, the correct option is:

vector

The energy stored in a capacitor (\(W\)) can be calculated using the formula:

\[ W = \dfrac{1}{2} \times C \times V^2 \]

Where:
- \( W \) is the energy stored,
- \( C \) is the capacitance,
- \( V \) is the voltage (emf) applied.

Given:
- \( C = 1 \) farad (capacitance),
- \( V = 4 \) volts (voltage).

Substituting the values into the formula:

\[ W = \dfrac{1}{2} \times 1 \times (4)^2 \]\[ W = \dfrac{1}{2} \times 1 \times 16 \]\[ W = 8 \, \text{joules} \]

So, the capacitor will store energy of 8 joules.

Therefore, the correct option is:

8 joules

To find the capacitance per meter (\( C \)) of the concentric cable capacitor, we can use the formula for capacitance of a coaxial capacitor:

\[ C = \dfrac{{2\pi\varepsilon_r\varepsilon_0}}{{\ln \left( \dfrac{b}{a} \right)}} \]

Where:
- \( \varepsilon_r \) is the relative permittivity of the insulation material,
- \( \varepsilon_0 \) is the vacuum permittivity (\( \varepsilon_0 \approx 8.854 \times 10^{-12} \, \text{F/m} \)),
- \( a \) is the radius of the inner cylinder,
- \( b \) is the radius of the outer cylinder.

Given:
- \( a = \dfrac{3}{2} \) mm,
- \( b = 5 \) mm (since the radius of the outer cylinder is 10 mm),
- \( \varepsilon_r = 3 \).

Substituting the values into the formula:

\[ C = \dfrac{{2\pi \times 3 \times 8.854 \times 10^{-12}}}{{\ln \left( \dfrac{5}{\dfrac{3}{2}} \right)}} \]

\[ C = \dfrac{{2\pi \times 3 \times 8.854 \times 10^{-12}}}{{\ln \left( \dfrac{10}{3} \right)}} \]

\[ C = \dfrac{{2\pi \times 3 \times 8.854 \times 10^{-12}}}{{\ln \left( \dfrac{10}{3} \right)}} \]

\[ C = \dfrac{{2\pi \times 3 \times 8.854 \times 10^{-12}}}{{\ln (3.333)}} \]

\[ C \approx \dfrac{{2\pi \times 3 \times 8.854 \times 10^{-12}}}{{1.204}} \]

\[ C \approx 13.88 \times 10^{-12} \, \text{F/m} \]

\[ C \approx 138.8 \, \text{pF/m} \]

So, the capacitance per meter of the concentric cable capacitor is approximately \( 138.8 \, \text{pF/m} \).

The dielectric constant (relative permittivity) of glass typically falls within the range of 5 to 100. 

So, the correct option is:

5 to 100

The capacity of a capacitor bank used in power factor correction is typically expressed in terms of kilovolt-amperes reactive (kVAR). 

So, the correct option is:

kVAR