MHT CET · Physics · Current Electricity
Moving coil galvanometers \(\mathrm{M}_{1}\) and \(\mathrm{M}_{2}\) have resistance, number of turns, area of coil and magnetic field as follows.
\(\mathrm{R}_{1}=10 \Omega, \mathrm{R}_{2}=14 \Omega, \mathrm{N}_{1}=30, \mathrm{~N}_{2}=42\)
\(\mathrm{A}_{1}=3 \cdot 6 \times 10^{-3} \mathrm{~m}^{2}, \mathrm{~A}_{2}=1 \cdot 8 \times 10^{-2} \mathrm{~m}^{2},\) \(\mathrm{~B}_{1}=0 \cdot 25 \mathrm{~T}, \mathrm{~B}_{2}=0 \cdot 50 \mathrm{~T}\)
(Spring constants are same for both materials)
The ratio of (i) current sensitivity and (ii) voltage sensitivity for galvanometer
\(\left(\mathrm{M}_{2}\right.\) to \(\left.\mathrm{M}_{1}\right)\) is respectively
- A \(1: 1, \quad 1 \cdot 4: 1\)
- B \(1: 1 \cdot 4\), \(1: 1\)
- C \(4: 1\) \(1: 1\)
- D \(1 \cdot 4: 1\) \(1: 1\)
Answer & Solution
Correct Answer
(D) \(1 \cdot 4: 1\) \(1: 1\)
Step-by-step Solution
Detailed explanation
(D)
We know, \(\mathrm{L}=\mu_{0} \mathrm{~N}^{2} \frac{\mathrm{A}}{\ell}\)
If \(x\) is the length of the wire and \(a\) is the area of cross section
\(\mathrm{R}=\frac{\rho \mathrm{x}}{\mathrm{a}} \quad \mathrm{m}=\mathrm{axD}\)
\(\mathrm{Rm}=\frac{\rho \mathrm{x}}{\mathrm{a}} \times \mathrm{axD} \quad \therefore \quad \mathrm{x}=\sqrt{\frac{\mathrm{Rm}}{\rho \mathrm{D}}}\)
Also,\(x=2 \pi r N\therefore \quad \mathrm{N}=\frac{\mathrm{x}}{2 \pi \mathrm{r}}\)
\(=\mu_{0}\left(\frac{\mathrm{x}}{2 \pi \mathrm{r}}\right)^{2} \frac{\pi \mathrm{r}^{2}}{\ell}=\frac{\mu_{0}}{4 \pi \ell} \frac{\mathrm{Rm}}{\rho \mathrm{D}}\)
We know, \(\mathrm{L}=\mu_{0} \mathrm{~N}^{2} \frac{\mathrm{A}}{\ell}\)
If \(x\) is the length of the wire and \(a\) is the area of cross section
\(\mathrm{R}=\frac{\rho \mathrm{x}}{\mathrm{a}} \quad \mathrm{m}=\mathrm{axD}\)
\(\mathrm{Rm}=\frac{\rho \mathrm{x}}{\mathrm{a}} \times \mathrm{axD} \quad \therefore \quad \mathrm{x}=\sqrt{\frac{\mathrm{Rm}}{\rho \mathrm{D}}}\)
Also,\(x=2 \pi r N\therefore \quad \mathrm{N}=\frac{\mathrm{x}}{2 \pi \mathrm{r}}\)
\(=\mu_{0}\left(\frac{\mathrm{x}}{2 \pi \mathrm{r}}\right)^{2} \frac{\pi \mathrm{r}^{2}}{\ell}=\frac{\mu_{0}}{4 \pi \ell} \frac{\mathrm{Rm}}{\rho \mathrm{D}}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- The magnetic field inside a current carrying toroidal solenoid is \(0.2 \mathrm{mT}\). What is the magnetic field inside the toroid if the currentMHT CET 2021 Medium
- When a monochromatic ray of light is passed through an equilateral glass prism, it is found that the refracted ray in glass is parallel to the base of the prism. If ' \(i\) ' and ' \(e\) ' denote the angles of incidence and emergence respectively, thenMHT CET 2023 Easy
- A metal conductor of length \(1 \mathrm{~m}\) rotates vertically about one of its ends at an angular velocity of \(5 \mathrm{rad} / \mathrm{s}\). if horizontal component of earth's magnetic field is \(0.2 \times 10^{-4} \mathrm{~T}\), then the e.m.f. developed between the two ends of the conductor isMHT CET 2021 Easy
- In series LCR circuit, at resonance the peak value of current will be \(\left[E_0\right.\) is peak emf, \(R\) is resistance, \(\omega L\) is inductive reactance, and \(1 / \omega \mathrm{C}\) is capacitive reactance]MHT CET 2021 Easy
- A mass attached to a spring performs S.H.M. whose displacement is \(\mathrm{x}=3 \times 10^{-3} \cos 2 \pi \mathrm{t}\) metre. The time taken to obtain maximum speed for the first time isMHT CET 2025 Medium
- A particle is performing a uniform circular motion along a circular of radius ' \(\mathrm{R}\) '. In half the period of revolution, its displacement and distance covered are respectivelyMHT CET 2021 Hard
More PYQs from MHT CET
- \(\lim _{x \rightarrow x}\left[\frac{\sqrt{x}-1}{\log x}\right]=\)MHT CET 2021 Easy
- Two inductors of \(60 \mathrm{mH}\) each are joined in parallel. The current passing through this combination is \(2.2 \mathrm{~A}\). The energy stored in this combination of inductors in joule isMHT CET 2023 Medium
- Given below are the two statements regarding photoreceptor cells of human eye.
Statement I: The three types of cone cells have their own characteristic photopigments that respond to red, green and blue lights.
Statement II: Sensation of white light is produced due to simultaneous equal stimulation of all three types of cone cells.
In the light of above statements, choose the correct answer from the options given below:MHT CET 2024 Medium - The intensity ratio of the maxima and minima in an interference pattern produced by two coherent sources of light is \(9: 1\). The intensities of the light sources used are in the ratioMHT CET 2024 Easy
- A particle moves along a straight line according to the law \(s=16-2 t+3 t^{3}\), where \(s\) metres is the distance of the particle from a fixed point at the end of \(t\) second. The acceleration of the particle at the end of \(2 \mathrm{~s}\) isMHT CET 2011 Easy
- If \(e_{1}\) and \(e_{2}\) represent the eccentricity of the curves \(16 x^{2}-9 y^{2}=144\) and \(9 x^{2}-16 y^{2}=144\)
respectively. Then, \(\frac{1}{e_{1}^{2}}+\frac{1}{e_{2}^{2}}\) is equal toMHT CET 2010 Easy