CBSE 2024 · Region 3 · Set 1 · Q32 · 5 marks
(i)(1)What is meant by current sensitivity of a galvanometer ? Mention the factors on which it depends.(2)A galvanometer of resistance G is converted into a voltmeter of range ( $\displaystyle 0-\mathrm{V}$ ) by using a resistance R . Find the resistance, in terms of $\displaystyle R$ and $\displaystyle G$, required to convert it into a voltmeter of range $\displaystyle \left(0-\frac{\mathrm{V}}{2}\right)$.(ii)The magnetic flux through a coil of resistance $\displaystyle 5 \Omega$ increases with time as : \[\phi=\left(2.0 \mathrm{t}^{3}+5.0 \mathrm{t}^{2}+6.0 \mathrm{t}\right) \mathrm{mWb} \] Find the magnitude of induced current through the coil at $\displaystyle \mathrm{t}=2 \mathrm{~s}$.(i)A rectangular coil of N turns and area of cross-section A is rotated at a steady angular speed $\displaystyle \omega$ in a uniform magnetic field. Obtain an expression for the emf induced in the coil at any instant of time.(ii)Two coplanar and concentric circular loops $\displaystyle \mathrm{L}_{1}$ and $\displaystyle \mathrm{L}_{2}$ are placed coaxially with their centres coinciding. The radii of $\displaystyle \mathrm{L}_{1}$ and $\displaystyle \mathrm{L}_{2}$ are $\displaystyle 1$ cm and $\displaystyle 100$ cm respectively. Calculate the mutual inductance of the loops. (Take $\displaystyle \pi^{2}=10$ )
(i)
(1)
What is meant by current sensitivity of a galvanometer ? Mention the factors on which it depends.
(2)
A galvanometer of resistance G is converted into a voltmeter of range ( $\displaystyle 0-\mathrm{V}$ ) by using a resistance R . Find the resistance, in terms of $\displaystyle R$ and $\displaystyle G$, required to convert it into a voltmeter of range $\displaystyle \left(0-\frac{\mathrm{V}}{2}\right)$.
(ii)
The magnetic flux through a coil of resistance $\displaystyle 5 \Omega$ increases with time as : \[\phi=\left(2.0 \mathrm{t}^{3}+5.0 \mathrm{t}^{2}+6.0 \mathrm{t}\right) \mathrm{mWb} \] Find the magnitude of induced current through the coil at $\displaystyle \mathrm{t}=2 \mathrm{~s}$.
(i)
A rectangular coil of N turns and area of cross-section A is rotated at a steady angular speed $\displaystyle \omega$ in a uniform magnetic field. Obtain an expression for the emf induced in the coil at any instant of time.
(ii)
Two coplanar and concentric circular loops $\displaystyle \mathrm{L}_{1}$ and $\displaystyle \mathrm{L}_{2}$ are placed coaxially with their centres coinciding. The radii of $\displaystyle \mathrm{L}_{1}$ and $\displaystyle \mathrm{L}_{2}$ are $\displaystyle 1$ cm and $\displaystyle 100$ cm respectively. Calculate the mutual inductance of the loops. (Take $\displaystyle \pi^{2}=10$ )
Marking-scheme solution
(i)
($\displaystyle 1$). Current sensitivity of galvanometer is defined as the deflection per unit current.
Alternatively,
\[\frac{\phi}{I}=\frac{N B A}{K}
\]
Factors
Number of turns in coil, Magnetic field intensity, Area of coil, Torsional Constant
Electromagnetic InductionFaraday’s Law of InductionApplylong_answerhard
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CBSE Class 12 Physics past-paper question from the 2024board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.