A 30 μF capacitor is connected to a 240 V, 50 Hz source. If the frequency of the source is changed from 50 Hz to 200 Hz, the capacitive reactance of the capacitor will
Show Hint
- increase by a factor of two.
- increase by a factor of four.
- decrease by a factor of four.
- decrease by a factor of two.
The Correct Option is C
Solution and Explanation
Step 1: Understanding capacitive reactance.
The capacitive reactance (\( X_C \)) is given by the formula:
\[
X_C = \frac{1}{2 \pi f C}
\]
where \( f \) is the frequency of the source, and \( C \) is the capacitance.
Step 2: Analyzing the change in frequency.
If the frequency is increased from 50 Hz to 200 Hz, the capacitive reactance will decrease because it is inversely proportional to the frequency. Specifically, if the frequency quadruples, the reactance will decrease by a factor of four.
Step 3: Conclusion.
The correct answer is (C) decrease by a factor of four, as the capacitive reactance is inversely proportional to frequency.
Top IIT JAM BT Physics Questions
- Rain is falling vertically with a speed of 40 $m s^{-1}$. Wind starts blowing with a speed of 16 $m s^{-1}$ in the west to east direction. How should a person, who is standing, hold his umbrella to avoid getting wet?
- A massless ideal spring is hanging vertically. A sphere of mass of 500 g, suspended from the spring, stretches the spring from its initial position by 50 cm when it reaches equilibrium. The force constant of the spring is _________ $N m^{-1}$. ($Use g=10 m s^{-2}$)
- Whales can dive undersea to depths of 2 km. The pressure on the whale at this depth (ignoring atmospheric pressure) is _____ $× 10^6 Pa$. (Density of sea water = $1 g cm^{-3}$ and $g =10 m s^{-2}$)
- The heat required to convert 2 kg of water at 20 °C in a calorimeter to steam at 100 °C and at atmospheric pressure (1 atm) is _____ kJ. (Specific heat capacity of water is $4.2 kJ kg^{-1} K^{-1}$ and latent heat of steam is $2256 kJ kg^{-1}$)
- An electron is accelerated from rest through a potential difference of 200 V. The de Broglie wavelength associated with this electron is _____ nm. (Rounded off to 2 decimal places) (Planck’s constant = $6.6 × 10^{-34} J s, 1eV=1.6 × 10^{-19} J$, mass of an electron = $9.1×10^{-31} kg$)
Top IIT JAM BT Combination of Resistors - Series and Parallel Questions
- Two resistors 2 Ω and 4 Ω are combined in parallel. If this combination is connected to a battery of 16 𝑉, the maximum current that can be drawn from the battery is ________ 𝐴 (rounded off to the nearest integer).
The equivalent capacitance of the following assembly of capacitors is .......... \( \mu F \).
The logic operation (OR, AND, NOR or NAND) carried out by the following circuit is
Top IIT JAM BT Questions
- Which one of the following compounds inhibits the polymerization of tubulin to microtubules in animal cells?
- Arrange the following elements in increasing order of their electronegativity according to the Pauling scale
C, Na, Be and Br - Which one of the following is NOT a plant vascular tissue?
- A growing shoot of a germinating seedling encounters an underground obstacle. Which one of the following hormones elicits ‘triple response’ to the underground obstacle?
- Which one of the following pairs of antibodies contains ‘J-chain’ in their multimeric form?