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प्रश्न
- A circular coil of 30 turns and radius 8.0 cm carrying a current of 6.0 A is suspended vertically in a uniform horizontal magnetic field of magnitude 1.0 T. The field lines make an angle of 60° with the normal of the coil. Calculate the magnitude of the counter torque that must be applied to prevent the coil from turning.
- Would your answer change, if the circular coil in (a) were replaced by a planar coil of some irregular shape that encloses the same area? (All other particulars are also unaltered.)
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उत्तर
(a) Number of turns on the circular coil, n = 30
Radius of the coil, r = 8.0 cm = 0.08 m
Area of the coil = πr2
= π(0.08)2
= 3.14 × 0.0064
= 0.0201 m2
Current flowing in the coil, I = 6.0 A
Magnetic field strength, B = 1 T
Angle between the field lines and normal with the coil surface,
θ = 60°
The coil experiences a torque in the magnetic field. Hence, it turns.
The counter torque applied to prevent the coil from turning is given by the relation,
τ = n IBA sin θ ...(i)
= 30 × 6 × 1 × 0.0201 × sin 60°
= `3.618 xx sqrt3/2`
= `3.618 xx 1.732/2`
= 3.618 × 0.866
= 3.133 N m
(b) It can be inferred from the relation (i) that the magnitude of the applied torque is not dependent on the shape of the coil. It depends on the area of the coil. Hence, the answer would not change if the circular coil in the above case is replaced by a planar coil of some irregular shape that encloses the same area.
संबंधित प्रश्न
The combined resistance of a galvanometer of resistance 500Ω and its shunt is 21Ω. Calculate the value of shunt.
Show that the current flowing through a moving coil galvanometer is directly proportional to the angle of deflection of coil.
Write the underlying principle of a moving coil galvanometer.
Why does a galvanometer show a momentary deflection at the time of charging or discharging a capacitor? Write the necessary expression to explain this observation.
Explain how moving coil galvanometer is converted into a voltmeter. Derive the necessary formula.
A rectangular coil of a moving coil galvanometer contains 100 turns, each having area
15 cm2. It is suspended in the radial magnetic field 0.03 T. The twist constant of suspension
fibre is 15 x 10-10 N-m/degree. Calculate the sensitivity of the moving coil galvanometer.
A galvanometer has a resistance of 16Ω. It shows full scale deflection, when a current of 20 mA is passed through it. The only shunt resistance available is 0.06 which is not appropriate to convert a galvanometer into an ammeter. How much resistance should be connected in series with the coil of galvanometer, so that the range of ammeter is 8 A?
Define current sensitivity of a galvanometer.
Define the current sensitivity of a galvanometer ?
A moving coil galvanometer has a coil of resistance 59 Ω. It shows a full-scale deflection for a current of 50 mA. How will you convert it to an ammeter having a range of 0 to 3A?
Define the term ‘current sensitivity’ of a moving coil galvanometer.
A galvanometer coil has a resistance of 12 Ω and the metre shows full scale deflection for a current of 3 mA. How will you convert the metre into a voltmeter of range 0 to 18 V?
Assertion (A): On Increasing the current sensitivity of a galvanometer by increasing the number of turns may not necessarily increase its voltage sensitivity.
Reason (R): The resistance of the coil of the galvanometer increases on increasing the number of turns.
Select the most appropriate answer from the options given below:
A multirange voltmeter can be constructed by using a galvanometer circuit as shown in figure. We want to construct a voltmeter that can measure 2V, 20V and 200V using a galvanometer of resistance 10Ω and that produces maximum deflection for current of 1 mA. Find R1, R2 and R3 that have to be used.
A voltmeter of variable ranges 3 V, 15 V, 150 V is to be designed by connecting resistances R1, R2, R3 in series with a galvanometer of resistance G = 20 Ω, as shown in Fig. The galvanometer gives full pass through its coil for 1 mA current i.e. "gives full pass through it's coil for 1 mA current". Then, the resistances R1, R2 and R3 (in kilo ohms) should be, respectively:
