Sheet 07 Moving Coil Galvanometer, Shunt, Ammeter and Voltmeter.
A current of \(300\mu A\) deflects the coil of a moving coil galvanometer by \(30^{o}\). (i)What should be the current to cause the rotation through \(\frac{\pi}{10}\) radians? (ii) What is the current sensitivity of galvanometer? (iii) If, the resistance of galvanometer is \(40\Omega\), find the voltage sensitivity.
Ans:(i) \(I_{2}=180\mu A\) (ii) \(I_{sensitivity}=0.17\frac{degree}{\mu A}\) and (iii) \(V_{sensitivity}=3400\frac{degree}{Volt}\).
If, the current sensitivity of a moving charge galvanometer is increased by \(20%\), its resistance increased by \(1\frac{1}{2}\) times. How will the voltage sensitivity of the galvanometer be affected?
Ans: \(V^{‘}_{sensitivity}=\frac{12}{25}V_{s}\).
A rectangular coil having each turn of length \(5cm\) and breadth \(4cm\) is suspended freely in a radial magnetic field of induction \(2.5\times10^{-2}Wb.m^{-2}\), torsional constant of the suspension fibre is \(1.5\times10^{-8}N.m.rad^{-1}\). The coil deflects through an angle of \(0.5\) radians when a current of \(2\mu A\) is passed through it. Find: the number of turns of coil?
Ans: \(N=75\).
To increase the current sensitivity of a moving charge galvanometer by \(50%\), its resistance is increased so that the new resistance becomes twice its initial resistance. By what factor its voltage sensitivity changes?
Ans: \(\Delta V_{s}=-\frac{1}{4}V_{s}\).
A galvanometer needs \(100mV\) for a full scale deflection of \(100\) divisions. Find: the voltage sensitivity. What must be the resistance of galvanometer if its current sensitivity is \(2division/\mu A\).
Ans: \(R_{s}=2000\Omega\).
Compare: the current sensitivity and the voltage sensitivity of the following moving charge galvanometer. Meter A: \(N=30\), \(A=1.5\times10^{-3}m^{2}\), \(B=0.25T\) and \(R=20\Omega\). Meter B: \(N=35\), \(A=2.0\times10^{-3}m^{2}\), \(B=0.25T\) and \(R=30\Omega\). Given: That the springs in two meters having the same torsional constants.
Ans: \(I_{sensitivity}=0.64\) and \(V_{sensitivity}=0.96\).
An ammeter of resistance \(0.80\Omega\) can measure the current up to \(1A\). (i) What must be the shunt resistance to enable the ammeter to measure the current up to \(5.0A\)? (ii) What is the combined resistance of the ammeter and the shunt?
Ans:(i) \(S=0.20\Omega\) and (ii) \(R_{A}=0.16\Omega\).
In a galvanometer there is a deflection of \(10\) divisions per mA. The internal resistance of the galvanometer is \(60\Omega\) If, a shunt of \(2.5\Omega\) is connected to the galvanometer and there are fifty divisions in all, on the scale of galvanometer, what maximum current can this galvanometer read?
Ans: \(I=125mA\).
The scale of a galvanometer is divided into \(150\) equal divisions. The galvanometer has the current sensitivity of \(10\) divisions per mA and the voltage sensitivity of \(2\) divisions. How the galvanometer can be designated to read; (i) \(\frac{6A}{division}\) ? (ii) \(\frac{1V}{division}\)?
Ans:(i) \(S=\left(8.3\times10^{-5}\right)\Omega\) and (ii) \(R=9995\Omega\).
A galvanometer of resistance ‘G’ can be converted into a voltmeter of range \(\left(\theta-V\right)\) volts by connecting a resistance of ‘R’ in series with it. How much resistance will be required to change its range from \(0\) to \(\frac{V}{2}\)?
Ans: \(R’=\frac{R-G}{2}\).
A galvanometer can be converted in to a voltmeter of certain range by connecting a resistance of \(1000\Omega\) in series with it. When the resistance of \(480\Omega\) connected in series, the range is halved. Find: the resistance of the galvanometer?
Ans: \(R_{galvanometer}=40\Omega\).
A galvanometer has a resistance of \(5\Omega\) and a full scale deflection is produced by \(15mA\). Calculate: what resistance should be connected with it so as to enable it to read: (a) \(1.5A\) and (b) \(1.5V\)?
Ans: \(S=0.0505\Omega\) and \(R=95\Omega\).
A galvanometer coil has a resistance of \(15.0\Omega\) and the meter shows full deflection for a current of \(2.0mA\). How will you convert the meter into (a) an ammeter of range \(0\) to \(5.0A\)? (b) a voltmeter of range \(0\) – \(15V\)? (c) Also calculate: the net resistance of galvanometer in each case?
Ans:(a) \(S=\left(6\times10^{-3}\right)\Omega\) (b) \(R=7485\Omega\) and (c) \(R_{V}=R+G=7500\Omega\).
A resistance of \(1980\Omega\) is connected in series with a voltmeter, after which the scale division becomes 100 times larger. Find: the resistance of the voltmeter.
Ans: \(R=20\Omega\).
A galvanometer of resistance \(50\Omega\) gives full scale deflection for a current of \(0.05A\). Calculate: the length of the wire required to convert the galvanometer into an ammeter of range \(0.5A\). The diameter lf the shunt wire is \(2mm\) and its resistivity is \(5\times10^{-7}\Omega-m\).
Ans: \(l=139.76m\).
A galvanometer has a resistance of \(100\Omega\). A resistance of \(1\Omega\) is connected across the terminals of the galvanometer. What part of the total current flow through the galvanometer. Draw the necessary circuit diagram.
Ans: \(I_{g}=\frac{I}{101}\).
A galvanometer having 30 divisions has a current sensitivity of \(20\mu A/division\). It has a resistance of \(25\Omega\). (a) How will you convert it into an ammeter upto \(1A\)? (b) How will you convert it into a voltmeter up to \(1V\).
Ans:(a) \(R_{A}=0.015\Omega\) and (b) \(R_{V}=0.985\Omega\).
A voltmeter reads \(5.0V\) at full scale deflection and its graded according to its resistance per unit volt at full scale deflection as \(5000\Omega .V^{-1}\). (i) How will you convert it into a voltmeter that reads \(20V\) at full scale deflection? (ii) Will it still be graded \(5000\Omega .V^{-1}\)? (iii)Will you prefer this voltmeter to one that is graded as \(2000\Omega .V^{-1}\)?
Ans:(i) \(75000\Omega\) (ii) \(Yes\) and (iii) \(preferred\).
A multirange current meter can be constructed by using a galvanometer circuit as shown in below figure. We want to current meter that can measure \(10mA\), \(100mA\) and \(1A\) using the galvanometer resistance \(10\Omega\) and that produces maximum deflection for current of \(1mA\). Find: \(S_{1}\), \(S_{2}\) and \(S_{3}\) that have to be used.
Ans: \(S_{1}=1\Omega\), \(S_{2}=0.1\Omega\) and \(S_{3}=0.01\Omega\).
A multirange voltmeter can be constructed by using a galvanometer circuit as shown in below figure. We want to construct a voltmeter that can measure \(2V\), \(20V\) and \(200V\) using a galvanometer of resistance \(10\Omega\) and that produces maximum deflection for a current of \(1mA\). Find: the value of \(R_{1}\), \(R_{2}\) and \(R_{3}\) that have to be used?
Ans: \(R_{1}=1990\Omega\), \(R_{2}=\left(18\times10^{3}\right)\Omega\) and \(R_{3}=\left(180\times10^{3}\right)\Omega\).
A voltmeter V of resistance \(400\Omega\) is used to measure the potential difference across a \(100\Omega\) in the given circuit below. (i) What will be the reading on the voltmeter? (ii) Calculate: the potential difference across \(100\Omega\) resistor before the voltmeter is connected?
Ans:(i) \(24V\) and (ii) \(V_{100\Omega}=28V\).
A d.c. supply of \(120V\) is connected to a large resistance X. A voltmeter of resistance \(10k\Omega\) placed in series in the circuit reads \(4V\). What s the value of X?
