A thick wire is stretched, so that its length become two times. Assuming that there is no change in its density, then what is the ratio of change in resistance of wire to the initial resistance of wire?
1
2:01
2
4:01
3
3:01
4
1:04
Official Solution
Correct Option: (3)
Resistance of the wire is given by
So, (If density remains same) or
Hence, change in resistance Therefore,
02
PYQ 2020
medium
physicsID: mht-cet-
Two coaxial coils A and B of radii and are placed in the same plane. ( ). If a current is passed through coil B, the coefficient of mutual inductance between the coils is proportional to
1
2
3
4
Official Solution
Correct Option: (3)
Step 1: Understanding mutual inductance. The mutual inductance between two coils is given by: where and are the radii of the coils, and is the distance between the coils. Step 2: Conclusion. Thus, the coefficient of mutual inductance between the coils is proportional to , which corresponds to option (C).
03
PYQ 2020
medium
physicsID: mht-cet-
Two coils of wire A and B are placed mutually perpendicular as shown. When current is changed in any one coil,
1
no current will be induced in another coil.
2
magnetic field will be perpendicular to plane of another coil.
3
magnetic flux linked with another coil is maximum.
4
current induced in another coil is maximum.
Official Solution
Correct Option: (1)
Step 1: Understanding electromagnetic induction. For electromagnetic induction to occur, the magnetic flux through the second coil must change. In this case, the coils are placed mutually perpendicular to each other, so when current in one coil changes, the flux through the second coil does not change. Therefore, no current will be induced in the second coil. Step 2: Conclusion. Thus, no current will be induced in another coil, corresponding to option (A).
04
PYQ 2020
medium
physicsID: mht-cet-
A bar magnet is held perpendicular to a uniform magnetic field. The couple acting on the magnet is to be halved by rotating it. Through what angle should it be rotated?
1
2
3
4
Official Solution
Correct Option: (4)
Step 1: Torque on a bar magnet.
Step 2: Initial condition. Initially, , so Step 3: New condition. Torque is halved: Step 4: Solving for angle.
Step 5: Conclusion.
05
PYQ 2020
medium
physicsID: mht-cet-
The coefficient of mutual induction is 2 H and induced e.m.f. across secondary is 2 kV. Current in the primary is reduced from 6 A to 3 A. The time required for the change of current is
1
2
3
4
Official Solution
Correct Option: (3)
Step 1: Formula for induced e.m.f. due to change in current. The induced electromotive force (e.m.f.) in the secondary coil is related to the rate of change of current in the primary coil by the equation: where is the mutual inductance, is the rate of change of current, and is the induced e.m.f. in the secondary. Step 2: Rearranging the equation. Solving for : Substituting the given values: Step 3: Finding the time. The change in current . Using , we can solve for : Step 4: Conclusion. Thus, the time required for the change of current is , corresponding to option (C).
06
PYQ 2020
medium
physicsID: mht-cet-
Two concentric circular coils having radii and are placed co-axially with centres coinciding. The mutual induction of the arrangement is (Both coils have single turn, = permeability of free space)
1
2
3
4
Official Solution
Correct Option: (4)
Step 1: Magnetic field at the centre of larger coil. Magnetic field due to a circular coil of radius at its centre is:
Step 2: Magnetic flux through smaller coil. Area of smaller coil:
Step 3: Mutual inductance.
Step 4: Conclusion. Mutual inductance of the arrangement is .
07
PYQ 2020
medium
physicsID: mht-cet-
A graph of magnetic flux versus current is shown for four inductors A, B, C, D. Smaller value of self inductance is for inductor
1
A
2
C
3
B
4
D
Official Solution
Correct Option: (4)
Step 1: Relation between magnetic flux and current. Self inductance is defined as: Thus, slope of the vs graph gives the value of self inductance.
Step 2: Comparing slopes of given graphs. From the graph, line A has the maximum slope, followed by B, then C, and D has the minimum slope.
Step 3: Conclusion. Since self inductance is directly proportional to slope, the smallest self inductance corresponds to the smallest slope, i.e. inductor D.
08
PYQ 2020
medium
physicsID: mht-cet-
A graph of magnetic flux ( ) versus current ( ) is shown for four inductors A, B, C and D. Larger value of self-inductance is for inductor
1
D
2
B
3
C
4
A
Official Solution
Correct Option: (4)
Step 1: Recall the relation of self-inductance. Self-inductance is given by the relation: Thus, the slope of the versus graph represents the self-inductance.
Step 2: Analyze the given graph. Among the four straight lines, inductor A has the steepest slope. A steeper slope means a larger value of .
Step 3: Conclusion. Inductor A has the maximum self-inductance.
09
PYQ 2020
medium
physicsID: mht-cet-
Capacity of a parallel plate air condenser is 2 ฮผF and voltage between the plates is changing at the rate of 3 V/s. The displacement current in the capacitor is
1
8 ฮผA
2
2 ฮผA
3
6 ฮผA
4
4 ฮผA
Official Solution
Correct Option: (3)
Step 1: Understanding displacement current. The displacement current in a capacitor is given by the formula:
where is the capacitance and is the rate of change of voltage across the plates. Step 2: Given values. We are given:
- Capacitance
- Rate of change of voltage Step 3: Calculating the displacement current. Substitute the given values into the formula for displacement current:
Step 4: Conclusion. The displacement current in the capacitor is 6 ฮผA, which corresponds to option (C).
10
PYQ 2020
medium
physicsID: mht-cet-
If is the number of turns in a circular coil, the value of its self-inductance varies as
1
2
3
4
Official Solution
Correct Option: (2)
Step 1: Definition of self-inductance. Self-inductance is defined as
Step 2: Dependence on number of turns. Magnetic flux linked with each turn is directly proportional to current and number of turns .
Step 3: Relation.
11
PYQ 2020
medium
physicsID: mht-cet-
A toroidal solenoid with air core has an average radius , number of turns and area of cross-section . The self-inductance of the solenoid is (Neglect the field variation across the cross-section of the toroid)
1
2
3
4
Official Solution
Correct Option: (2)
Step 1: Magnetic field inside a toroidal solenoid. For a toroid with air core, the magnetic field at mean radius is given by
Step 2: Magnetic flux through one turn.
Step 3: Calculate total flux linkage.
Step 4: Use definition of self-inductance.
12
PYQ 2020
medium
physicsID: mht-cet-
Alternating current of peak value A flows through the primary coil of transformer. The coefficient of mutual inductance between primary and secondary coil is 1 H. The peak e.m.f. induced in secondary coil is (Frequency of a.c. = 50 Hz)
1
400 V
2
200 V
3
300 V
4
100 V
Official Solution
Correct Option: (2)
Step 1: Using the formula for e.m.f. in a transformer. The induced e.m.f. in the secondary coil is given by: where is the mutual inductance and is the rate of change of current. For alternating current, the peak value of induced e.m.f. is given by: Substituting the given values: Step 2: Conclusion. The correct answer is (B), 200 V.
13
PYQ 2022
easy
physicsID: mht-cet-
Two coils P and S have a mutual inductance of 5 x 10-3 H. If the current in the coil, P is I = 10 sin (100 ฯt), then the maximum value of the e.m.f. induced in coil S is
1
6.28 V
2
12.56 V
3
15.70 V
4
3.14 V
Official Solution
Correct Option: (3)
Current in the coil is: Ip = I0 sin ฯt Now = I0ฯ cos ฯt e.m.f = M e.m.f = MIฯ cos ฯt Maximum value of the e.m.f. induced in coil: e.m.fmax = 5 x 10-3 x 10 x 100 ฯt x1 e.m.fmax = 5 x 10-3 x 103 x ฯt e.m.fmax = 5ฯ e.m.fmax = 5 x 3.14 e.m.fmax = 15.70 V Therefore the correct option is (C) 15.70 V.
14
PYQ 2022
easy
physicsID: mht-cet-
A galvanometer of resistance G has voltage range Vg. Resistance required to convert it to read voltage up to V is
1
(V- )G
2
G( -1)
3
G*
4
(V+ )G
Official Solution
Correct Option: (2)
The total resistance in the circuit is given by the sum of the galvanometer resistance and the series resistor: G + R. Using Ohm's Law, the current passing through the galvanometer can be calculated as I = Since we want to limit the current to be within the galvanometer's range, we have: I โค . Substituting the expression for I and rearranging the inequality, we get: โค Multiplying both sides by G and rearranging, we have: V โค * (G + R) V โค Vg + * R Now, subtracting Vg from both sides, we get: V - Vg โค * R Dividing both sides by , we have: โค R R โฅ (V - Vg) * R โฅ R โฅ - G R โฅ G*( - 1) Therefore, the correct option is (B) G( - 1), which represents the resistance required to convert the galvanometer to read voltage up to V.
15
PYQ 2022
easy
physicsID: mht-cet-
If โNโ is the number of turns in a circular coil, the value of its self-inductance varies as
1
N0
2
N3
3
N2
4
N1
Official Solution
Correct Option: (3)
The self-inductance, denoted by L, is given by: L = where: ฮผโ is the permeability of free space, N is the number of turns in the coil, A is the cross-sectional area of the coil, and l is the length of the coil. From the equation, We can see that the self-inductance (L) varies as the square of the number of turns (Nยฒ). Therefore, the correct answer is (C) Nยฒ.
16
PYQ 2023
hard
physicsID: mht-cet-
At the pure inductive stage, find emax.
Official Solution
Correct Option: (1)
At the pure inductive stage, the maximum voltage or can be determined by the equation:
where is the maximum current flowing through the inductor and is the inductive reactance.
Inductive reactance is calculated using the formula:
where is the frequency of the alternating current (AC) signal and is the inductance of the inductor.
To find , you would need to know the values of , , and for the specific circuit or scenario in question. Once you have those values, you can substitute them into the equations to calculate the maximum voltage or at the pure inductive stage.
17
PYQ 2024
medium
physicsID: mht-cet-
A wire of length moving with velocity at right angles to a magnetic field of . The magnitude of induced emf between the ends of the wire will be:
1
2
3
4
Official Solution
Correct Option: (4)
The induced emf in a conductor moving through a magnetic field is given by: where: is the magnetic field strength, is the velocity of the conductor, is the length of the conductor. Step 1: Substitute the Given Values Substitute , , and into the formula: Step 2: After Simplify Final Answer:
18
PYQ 2024
medium
physicsID: mht-cet-
Which of the following correctly represents the AND logic gate?
1
Output = 1 if at least one input is 1
2
Output = 1 only if all inputs are 1
3
Output = 0 if all inputs are 0
4
Output = 1 if all inputs are 0
Official Solution
Correct Option: (2)
The AND gate performs a logical multiplication. The output of an AND gate is: where and are the inputs.
Truth table:
19
PYQ 2024
medium
physicsID: mht-cet-
The magnetic flux through a coil perpendicular to its plane is varying according to the relation . If the resistance of the coil is , then the induced current through the coil at will be:
1
2
3
4
Official Solution
Correct Option: (1)
The induced EMF ( ) can be derived using Faraday's Law, which is expressed as: Given the magnetic flux:
Now, differentiate with respect to :
To calculate at :
Next, we apply Ohmโs Law to find the induced current :
Substitute into the equation:
Final Answer:
20
PYQ 2025
easy
physicsID: mht-cet-
A coil has 200 turns and an area of . If the magnetic field changes from 0 to 0.5 T in 0.1 seconds, what is the induced emf in the coil?
1
1 V
2
0.5 V
3
2 V
4
5 V
Official Solution
Correct Option: (1)
Given: Number of turns, Area of the coil, Change in magnetic field, Time taken for the change,
Step 1: Formula for Induced emf The induced emf in a coil due to a change in magnetic flux is given by Faradayรขโฌโขs Law: where is the change in magnetic flux.
Step 2: Calculate the Induced emf The change in magnetic flux is: Substitute into the formula for emf: The induced emf is (ignoring the negative sign since we are only interested in the magnitude).
Answer: The correct answer is option (a): 1 V.
21
PYQ 2025
hard
physicsID: mht-cet-
A circular coil of 50 turns, each of radius 0.1 m, carries a current of 2 A. If the coil is placed in a uniform magnetic field of 0.5 T perpendicular to its plane, what is the magnitude of the torque acting on the coil?
1
2
3
4
Official Solution
Correct Option: (2)
To find the torque acting on the coil, we use the formula for the torque on a current-carrying loop in a magnetic field: . Here,
is the number of turns ( ).
is the current ( ).
is the area of the coil ( with radius ).
is the magnetic field ( ).
is the angle between the plane of the coil and the magnetic field. Since the coil is perpendicular to the field, , and .
First, calculate the area :
.
Now substitute the values into the torque formula:
.
Finally, calculate the numeric value:
.
The magnitude of the torque acting on the coil is 0.785 Nยทm.
22
PYQ 2025
easy
physicsID: mht-cet-
A conducting rod of length L and mass m falls vertically under gravity through a region of uniform magnetic field B, directed into the plane of the page. The rod is placed on two smooth, vertical conducting rails connected at the bottom by a resistor R. Assuming no friction or air resistance, and the rod quickly reaches a constant terminal velocity, find the expression for v in terms of B, L, m, R.
1
2
3
4
Official Solution
Correct Option: (1)
The force on the rod due to gravity is . The magnetic force on the rod is given by , where is the induced current. The current is induced by the motion of the rod through the magnetic field, and the resistance is . According to Ohmรขโฌโขs law, the current is: At terminal velocity, the magnetic force balances the gravitational force: Substitute into this equation: Solve for : Thus, the expression for the velocity is .
23
PYQ 2025
medium
physicsID: mht-cet-
A wire of length having Resistance falls from a height in Earth's horizontal magnetic field. What is the current through the wire?
1
2
3
4
Official Solution
Correct Option: (1)
When the wire falls in Earth's magnetic field, an induced emf is generated due to the motion of the wire in the magnetic field. According to Faraday's Law of Induction, the induced emf ( ) is given by: where: - is the magnetic field, - is the velocity of the wire as it falls, and - is the length of the wire. The velocity of the wire can be determined using the equation for free fall: where is the acceleration due to gravity and is the height from which the wire falls. Substituting this into the equation for the induced emf: The current is given by Ohm's law: Thus, the current is proportional to the magnetic field , the height , and the length , and inversely proportional to the resistance . The correct expression for the current through the wire is .
