When you double capacitance and inductance, the new resonance frequency becomes halved.
What is Resonance frequency?
It is the natural frequency of an object where it tends to vibrate at a higher amplitude.
The resonance frequency of the LC series circuit is the frequency at which the capacity reactance is equal to inductive reactance.
The formula resonance frequency:
![f_{0} = \frac{1}{2\pi \sqrt{LC} }](https://tex.z-dn.net/?f=f_%7B0%7D%20%20%3D%20%5Cfrac%7B1%7D%7B2%5Cpi%20%5Csqrt%7BLC%7D%20%7D)
where;
f0 is the resonance frequency
L is the inductance
C is the capacitance
here, if the capacitance and inductance are doubled, the new resonance frequency becomes;
![f = \frac{1}{2\pi \sqrt{2L2C} }\\f = \frac{1}{2\pi \sqrt{4LC} }\\f = \frac{1}{2*2\pi \sqrt{LC} }\\f=\frac{1}{2} \frac{1}{2\pi \sqrt{LC} }\\f = \frac{1}{2} f_{0}](https://tex.z-dn.net/?f=f%20%20%3D%20%5Cfrac%7B1%7D%7B2%5Cpi%20%5Csqrt%7B2L2C%7D%20%7D%5C%5Cf%20%3D%20%5Cfrac%7B1%7D%7B2%5Cpi%20%5Csqrt%7B4LC%7D%20%7D%5C%5Cf%20%3D%20%5Cfrac%7B1%7D%7B2%2A2%5Cpi%20%5Csqrt%7BLC%7D%20%7D%5C%5Cf%3D%5Cfrac%7B1%7D%7B2%7D%20%20%5Cfrac%7B1%7D%7B2%5Cpi%20%5Csqrt%7BLC%7D%20%7D%5C%5Cf%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20f_%7B0%7D)
Thus from the above equation for frequency,
When you double capacitance and inductance, the new resonance frequency becomes f(0) / 2.
Learn more about resonance frequency here:
<u>brainly.com/question/15208335</u>
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Answer:
Option B is the correct answer.
Explanation:
Refer the figure we have centripetal force at bottom of circle
![F_c=F_t-F_w\\\\\frac{mv^2}{r}=F_t-mg\\\\F_t=m\left ( \frac{v^2}{r}+g\right )](https://tex.z-dn.net/?f=F_c%3DF_t-F_w%5C%5C%5C%5C%5Cfrac%7Bmv%5E2%7D%7Br%7D%3DF_t-mg%5C%5C%5C%5CF_t%3Dm%5Cleft%20%28%20%5Cfrac%7Bv%5E2%7D%7Br%7D%2Bg%5Cright%20%29)
We have mass, m = 2 kg
Radius, r = 1.2 m
For circular motion to occur we have tension at top = 0
That is
![\frac{mv^2}{r}=mg\\\\v=\sqrt{rg}](https://tex.z-dn.net/?f=%5Cfrac%7Bmv%5E2%7D%7Br%7D%3Dmg%5C%5C%5C%5Cv%3D%5Csqrt%7Brg%7D)
Now let us find tension at bottom point
![F_t=2\times \left ( \frac{rg}{r}+g\right )=4g=40N](https://tex.z-dn.net/?f=F_t%3D2%5Ctimes%20%5Cleft%20%28%20%5Cfrac%7Brg%7D%7Br%7D%2Bg%5Cright%20%29%3D4g%3D40N)
Option B is the correct answer.
Power = (voltage) x (current)
350 watts = (120 volts) x (current)
350 watts / 120 volts = current
current = 2.917 Amperes continuously
Answer:
Explanation:
a )
Work done by force = change in kinetic energy
F x s = ( vf² - vi² ) / 2m
F = ( vf² - vi² ) / 2ms
acceleration = ( vf² - vi² ) / 2m²s
b )
F = ( vf² - vi² ) / 2ms [ calculated above ]
c )
Work done by force
= change in kinetic energy
= ( vf² - vi² ) / 2m