A parallel plate capacitor having plate area 50 cm square and separation 0.1 mm is completely filled with the dielectric of dielectric constant 10 a capacitor is connected to 10 kilo ohm resistance and an alternative voltage we requested 10 sin 100 PT 3 of them connected in parallel or all of them are connected in parallel the switch s is closed and time is given by 2 by 5 second then find the ratio of displacement current in capacitor to the current in resistance?

Question

Answer

Given Parameters
- Plate Area (A) = 50 cm² = 50 × 10⁻⁴ m²
- Separation (d) = 0.1 mm = 0.1 × 10⁻³ m
- Dielectric Constant (κ) = 10
- Resistance (R) = 10 kΩ = 10 × 10³ Ω
- Voltage (V) = 10 sin(100πt)

Capacitance Calculation
The capacitance (C) of a parallel plate capacitor is given by:
$$ C = \frac{κ \cdot ε₀ \cdot A}{d} $$
Where:
- $ ε₀ $ (Permittivity of free space) = 8.85 × 10⁻¹² F/m
Calculating C:
$$
C = \frac{10 \cdot 8.85 \times 10^{-12} \cdot 50 \times 10^{-4}}{0.1 \times 10^{-3}} = 4.425 \times 10^{-9} F
$$

Displacement Current (I_d)
The displacement current (I_d) in a capacitor is given by:
$$ I_d = C \frac{dV}{dt} $$
Calculating $\frac{dV}{dt}$:
$$
V = 10 \sin(100πt) \implies \frac{dV}{dt} = 10 \cdot 100π \cos(100πt)
$$
Thus,
$$
I_d = 4.425 \times 10^{-9} \cdot 10 \cdot 100π \cos(100πt) = 4.425 \times 10^{-7} π \cos(100πt)
$$

Current Through Resistance (I_R)
Using Ohm's law, the current through the resistor (I_R) is given by:
$$ I_R = \frac{V}{R} = \frac{10 \sin(100πt)}{10 \times 10^3} = 10^{-3} \sin(100πt) $$

Ratio of Displacement Current to Resistance Current
The ratio of displacement current to the current in the resistor is:
$$
\text{Ratio} = \frac{I_d}{I_R} = \frac{4.425 \times 10^{-7} π \cos(100πt)}{10^{-3} \sin(100πt)}
$$
This ratio varies with time due to the cos and sin functions but represents the relationship between the two currents in the circuit.

Similar Physics Doubts

Polarization in a dielectric on application of electric field is

In a simple circuit for charging of a capacitor of 100 µF through a resistance of 10 kΩ in series by a battery of 6 volt in your laboratory, the displacement current id between the capacitor plates after 500 millisecond shall be?

In a non-magnetic dielectric medium with dielectric constant = 4, the electric field of a propagating plane wave with omega= 10^8 rad/s is given by. E = (-i+√3j) exp[j(omega.t-k.r)] The propagation vector k is given by?

Top Courses for Physics

Suggested Free Tests

Related Content

Schools

Competitive Examinations

Quick Access Links

Technical Exams