Download App

Electrostatic Potential and Capacitance — Physics STD 12 Science — Question

Bihar BoardEnglish MediumSTD 12 SciencePhysicsElectrostatic Potential and Capacitance4 Marks
Question
The saturation current from a thoriated-tungsten cathode at 2000K is 100mA. What will be the saturation current for a pure-tungsten cathode of the same surface area operating at the same temperature? The constant A in the Richardson-Dushman equation is 60 × 104Am-2K-2 for pure tungsten and 3.0 × 104Am-2k-2 for thoriated tungsten. The work function of pure tungsten is 4.5eV and that of thoriated tungsten is 2.6eV.
✓

Answer

$\text{i}=\text{AST}^2\text{ e}^{\frac{-\phi}{\text{KT}}}$
$\text{i}_1=\text{i},\ \text{i}_2=100\text{mA}$
$\text{A}_1=60\times10^4,\ \text{A}_2=3\times10^4$
$\text{S}_1=\text{S},\ \text{S}_2=\text{S}$
$\text{T}_1=2000,\ \text{T}_2=2000$
$\phi_1=4.5\text{eV},\ \phi_2 =2.6\text{eV}$
$\text{i}=(60\times10^{4})(\text{S})\times(2000)^2\frac{-45\times1.6\times10^{-19}}{\text{e}^{1.38\times10^{-23}\times2000}}$
$100=(3\times10^{4})(\text{S})\times(2000)^2\frac{-2.6\times1.6\times10^{-19}}{\text{e}^{1.38\times10^{-23}\times2000}}$
Dividing the equation,
$\Rightarrow\frac{\text{i}}{100}=\text{e}^{\big[\frac{-4.5\times1.6\times10}{1.38\times2}\big(\frac{-2.6\times1.6\times10}{1.38\times20}\big)\big]}$
$\Rightarrow\frac{\text{i}}{100}=20\times\text{e}^{-11.014}$
$\Rightarrow\frac{\text{i}}{100}=20\times0.000016$
$\Rightarrow\text{i}=20\times0.0016=0.0329\text{mA}=33\mu\text{A}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "4 Marks Questions" from Electrostatic Potential and Capacitance→Electrostatic Potential and Capacitance — all question types→Physics STD 12 Science question papers→Bihar Board STD 12 Science question papers→Bihar Board question paper generator→

Similar questions

A horizontal overhead power line carries a current of 90 A in east to west direction. What is the magnitude and direction of magnetic field due to the current 1.5 m in below the line?
→
Light of wavelength 488 nm is produced by an argon laser which is used in the photoelectric effect. When light from this spectral line is incident on emitter, the stopping (cut-off) potential of photoelectrons is 0.38 V. Find the work function of the material from which material is made.
→
To convert two atoms into ions, 2 electrons have been removed from each of them. When these ions are placed in a vacuum, they repel each other with a force of $3.7 \times 10^{-9}$ Newton. Find the distance between them.
→

According to Einstein, when a photonoflight offrequencyu or wavelength $\lambda$ is incident on a photosensitive metal surface of work function $\phi_0$, where $\phi_0<\text{h}\upsilon$ (here, h is Planck's constant), then the emission of photoelectrons takes place. The maximum kinetic energy of the emitted photoelectrons is given by $\text{K}_\text{max}=\text{h}\upsilon-\phi_0$. If the frequency of the incident light is $\upsilon_0$ called thresold frequency, the photoelectrons are emitted from metal without any kinetic energy. So $\text{h}\upsilon_0=\phi_0$.

  1. A metal of work function 3.3eV is illuminated by light of wavelength 300nm. The maximum kinetic energy of photoelectrons emitted is (taking h = 6.6 × 10-34 Js).
  1. 0.413eV
  2. 0.825eV
  3. 1.65eV
  4. 1.32eV

  1. The variation of maximum kinetic energy (Kmax) of the variation of maximum kinetic energy ($\upsilon$) of the incident radiations can be represented by:

  1. The variation of photoelectric current (i) with the intensity of the incident radiation (I) can be represented by:

  1. The graph between the stopping potential (V0) and $\Big(\frac{1}{\lambda}\Big)$ is shown in the figure. $\phi_1,\phi_2,\phi_3$ are work function. Which of the following options is correct?

  1. $\phi_1:\phi_2:\phi_3=1:2:3$

  2. $\phi_1:\phi_2:\phi_3=4:2:1$

  3. $\phi_1:\phi_2:\phi_3=1:2:4$

  4. Ultraviolet tight can be used to emit photoelectrons from metal 2 and metal 3 only.
  1. Which of the following figures represent the variation of particle momentum and the associated de-Broglie wavelength?

→
No part of India is situated on the equator. Is it possible to have a geostationary satellite which always remains over New Delhi?
→
Step-down transformers are used to decrease or step-down voltages. These are used when voltages need to be lowered for use in homes and factories. A small town with a demand of 800kW of electric power at 220V is situated 15km away from an electric plant generating power at 440V. The resistance of the two wire line carrying power is 0.5Q per km. The town gets power from the line through a 4000 - 220V step-down transformer at a sub-station in the town.

  1. The value of total resistance of the wires is:
  1. $25\Omega$
  2. $30\Omega$
  3. $35\Omega$
  4. $15\Omega$
  1. The line power loss in the form of heat is:
  1. 550kW
  2. 650kW
  3. 600kW
  4. 700kW
  1. How much power must the plant supply, assuming there is negligible power loss due to leakage?
  1. 600kW
  2. 1600kW
  3. 500W
  4. 1400kW
  1. The voltage drop in the power line is:
  1. 1700V
  2. 3000V
  3. 2000V
  4. 2800V
  1. The total value of voltage transmitted from the plant is:
  1. 500V
  2. 4000V
  3. 3000V
  4. 7000V
→
Motion of Charge in Magnetic Field
An electron with speed $V_0$ << c moves in a circle of radius $r _{\circ}$ in a uniform magnetic field. This electron is able to traverse a circular path as the magnetic force acting on the electron is perpendicular to both $V_0$ and B ,as shown in the figure. This force continuously deflects the particle sideways without changing its speed and the particle will move along a circle perpendicular to the field. The time required for one revolution of the electron is $T _{ o }$.

Image

(i) If the speed of the electron is now doubled to 2vo. The radius of the circle will change to
(A) $4 r_0$ (B) $2 r_0$ (C) $r _{ o }$ (D) $r _0 / 2$

(ii) If v = 2vo, then the time required for one revolution of the electron (To ) will change to
(A) $4 T_0$ (B) $2 T_{ O }$ (C) $T _{ o }$ (D) $T _{ d } / 2$
(iii) A charged particles is projected in a magnetic field . The acceleration of the particle is found to be. Find the value of x.
(A) $4 ms^{-2}$ (B) $-4 ms^{-2}$ (C) $-2 ms^{-2}$ (D) $2 ms^{-2}$

(iv) If the given electron has a velocity not perpendicular to B, then trajectory of the electron is
(A) straight line (B) circular (C) helical (D) zig-zag

OR

If this electron of charge (e) is moving parallel to uniform magnetic field with constant velocity v, the force acting on the electron is
(A) Bev (B) Be/v (C) B/ev (D) Zero
→
A narrow pencil of parallel light is incident normally on a solid transparent sphere of radius r. What should be the refractive index if the pencil is to he focused.
  1. At the surface of the sphere.
  2. At the centre of the sphere.
→
Define eddy currents. How are they produced? In what sense are these currents undesirable in a transformer and how are these reduced in a device ?
→
A short magnet oscillates in an oscillation magnetometern with a time period of 0.10s where the earth's horizontal magnetic field is $24\mu\text{T}.$ A downward current of 18 A is established in a vertical wire placed 20cm east of the magnet. Find the new time period.
→