Electromagnetism - SS2 Physics Past Questions and Answers - page 4
In an RC circuit, the time constant represents:
The time taken for the capacitor to charge to its maximum voltage
The time taken for the capacitor to discharge completely
The time taken for the circuit to reach steady-state conditions
The time taken for the voltage across the capacitor to decrease by 37% of its initial value
Explanation: The time constant represents the time taken for the voltage across the capacitor to increase or decrease by approximately 63.2% (1 - 1/e) of its initial or final value.
In an RC circuit, if the capacitance is doubled while the resistance remains constant, what happens to the time constant?
Doubles
Halves
Remains the same
Increases by a factor of 4
Explanation: The time constant (τ) of an RC circuit is inversely proportional to the product of resistance (R) and capacitance (C). If C is doubled while R remains constant, τ = RC is doubled as well.
In an RC circuit, a 100 μF capacitor is connected in series with a 10 kΩ resistor. Calculate the time constant of the circuit.
The time constant (τ) of an RC circuit is given by the product of resistance (R) and capacitance (C). τ = RC = (10,000 Ω) × (100 × 10^(-6) F) = 1 s.
In an RC circuit, a 220 Ω resistor is connected in series with a 47 μF capacitor. Calculate the time constant of the circuit.
The time constant (τ) of an RC circuit is given by the product of resistance (R) and capacitance (C). τ = RC = (220 Ω) × (47 × 10(-6) F) = 10.34 ms.
An RC circuit with a time constant of 5 ms is connected to a 100 V DC power supply. Calculate the voltage across the capacitor after one time constant.
After one-time constant (τ), the voltage across the capacitor will reach approximately 63.2% of its final value. Therefore, the voltage across the capacitor after one time constant is 0.632 × 100 V = 63.2 V.
In an RC circuit, the capacitor is initially charged to 200 V. If the time constant of the circuit is 3 ms, calculate the voltage across the capacitor after 6 ms.
After two time constants (2τ), the voltage across the capacitor will reach approximately 86.5% of its final value. Therefore, the voltage across the capacitor after 6 ms is 0.865 × 200 V = 173 V.
A positively charged particle moves in a magnetic field. If the magnetic force acting on the particle is zero, which of the following statements is true?
The particle is not moving.
The particle is moving parallel to the magnetic field.
The particle is moving perpendicular to the magnetic field.
The particle is moving opposite to the direction of the magnetic field.
Explain the concept of a magnetic field and how it affects charged particles in motion. Provide examples to illustrate your explanation.
A magnetic field is a region in space where magnetic forces are exerted on charged particles. It is created by moving charges or current-carrying conductors. When a charged particle moves through a magnetic field, it experiences a magnetic force perpendicular to both its velocity vector and the magnetic field direction. This force follows the right-hand rule, where the thumb points in the direction of the particle's velocity, the fingers point in the direction of the magnetic field, and the palm represents the direction of the magnetic force. This force can cause the particle to change its direction or move in a circular path, depending on the relative directions of the velocity and magnetic field.
For example, consider a positive charge moving to the right in a uniform magnetic field directed into the page. The magnetic force acting on the charge is directed downwards due to the right-hand rule. As a result, the charge experiences a centripetal force towards the centre of its circular path, causing it to move in a circle.
Discuss the motion of charged particles in magnetic fields and explain how their trajectory is affected by various factors.
The motion of charged particles in magnetic fields depends on various factors, including the velocity of the particle, the magnetic field strength, and the angle between the velocity and magnetic field direction.
When a charged particle moves parallel or antiparallel to the magnetic field, it experiences no magnetic force. However, when the particle's velocity has a component perpendicular to the magnetic field, it experiences a magnetic force that causes it to move in a circular path. The radius of this path depends on the particle's velocity, the magnetic field strength, and the mass-to-charge ratio of the particle.
The trajectory of a charged particle can be affected by the angle between its velocity and the magnetic field. When the velocity is at an angle to the magnetic field, the particle moves along a helical path, combining the circular motion and the original direction of motion. The pitch of the helix depends on the angle and the ratio of the particle's charge to its mass.
Additionally, the motion of charged particles in magnetic fields can be used to determine their charge-to-mass ratio in devices like mass spectrometers or to deflect charged particles in particle accelerators.
When a magnet is moved toward a loop of wire, which of the following best describes the induced current in the wire?
The induced current flows clockwise.
The induced current flows counterclockwise.
There is no induced current.
The direction of the induced current depends on the speed of the magnet.