A 6.50 × 10–3 m2 piston compresses gas in a cylinder with a surface area of 9.75 × 10–2 m2. What is the force on the cylinder wa
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Answer: a) 1 b) 61 W c) 61 W
Explanation:
a) The Power Factor (also known as cos φ), is defined by the difference in phase between current and voltage, in a RLC series circuit, and is expressed as follows:
cos φ = R / Z = R /
In resonance, XL =XC, so the circuit behaves like it were purely resistive, so Z=R.
Replacing in the expression for power factor, we have:
cos φ = R/Z = R/R = 1
This means that in resonance, current and voltage are in phase each other.
b) The average power delivered by the source, in resonance, is simply the power dissipated at the resistance R, as follows:
Pavg = V² rms / R = V₀² / √2 / R = 61 W
c) If the circuit remains in resonance, the average power , which does not depends on frequency provided this condition remains, keeps the same, i.e. , 61 W.
Answer:
The induced emf in the short coil during this time is 1.728 x 10⁻⁴ V
Explanation:
The magnetic field at the center of the solenoid is given by;
B = μ(N/L)I
Where;
μ is permeability of free space
N is the number of turn
L is the length of the solenoid
I is the current in the solenoid
The rate of change of the field is given by;
The induced emf in the shorter coil is calculated as;
where;
N is the number of turns in the shorter coil
A is the area of the shorter coil
Area of the shorter coil = πr²
The radius of the coil = 2.5cm / 2 = 1.25 cm = 0.0125 m
Area of the shorter coil = πr² = π(0.0125)² = 0.000491 m²
E = 14 x 0.000491 x 0.02514
E = 1.728 x 10⁻⁴ V
Therefore, the induced emf in the short coil during this time is 1.728 x 10⁻⁴ V