Power = (work done) / (time to do the work)
= (21,000 Joules) / (30 seconds)
= (21,000 / 30) joule/sec
= 700 watts
Answer:
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Explanation:
It does not affect the objects potential energy.
Answer:
C
Explanation:
the formula is a + b = ab
Answer:
The maximum voltage across the inductor is ![V_i = 0.136 V](https://tex.z-dn.net/?f=V_i%20%3D%200.136%20V)
Explanation:
From the question we are told that
The amplitude of the power is ![E_o = 180.0V](https://tex.z-dn.net/?f=E_o%20%3D%20180.0V)
The resistance is ![R = 90 \Omega](https://tex.z-dn.net/?f=R%20%3D%2090%20%5COmega)
The capacitance is ![C= 5.4 F](https://tex.z-dn.net/?f=C%3D%205.4%20F)
The inductance is ![L = 25.0mH = 25 *10^{-3} H](https://tex.z-dn.net/?f=L%20%3D%2025.0mH%20%3D%2025%20%2A10%5E%7B-3%7D%20H)
According to the question the the circuit frequency is resonance frequency
At resonance frequency
capacitive Reactance is equal to the Inductive Reactance
The capacitive Reactance is mathematically represented as
![X_c = \frac{1}{wC}](https://tex.z-dn.net/?f=X_c%20%3D%20%5Cfrac%7B1%7D%7BwC%7D)
Where ![w = \frac{1}{\sqrt{LC} }](https://tex.z-dn.net/?f=w%20%3D%20%5Cfrac%7B1%7D%7B%5Csqrt%7BLC%7D%20%7D)
Substituting values
![w = \frac{1}{\sqrt{5.4 * 25 *10^{-2}} }](https://tex.z-dn.net/?f=w%20%3D%20%5Cfrac%7B1%7D%7B%5Csqrt%7B5.4%20%2A%2025%20%2A10%5E%7B-2%7D%7D%20%7D)
![w = \frac{1}{\sqrt{5.4 * 25 *10^{-2}} }](https://tex.z-dn.net/?f=w%20%3D%20%5Cfrac%7B1%7D%7B%5Csqrt%7B5.4%20%2A%2025%20%2A10%5E%7B-2%7D%7D%20%7D)
![w = 2.72\ rad /s](https://tex.z-dn.net/?f=w%20%3D%202.72%5C%20%20rad%20%2Fs)
So ![X_c = \frac{1}{2.72 * 5.4 }](https://tex.z-dn.net/?f=X_c%20%3D%20%5Cfrac%7B1%7D%7B2.72%20%2A%205.4%20%7D)
![X_c =0.068](https://tex.z-dn.net/?f=X_c%20%3D0.068)
The inductive Reactance is mathematically represented as
![X_L = wL](https://tex.z-dn.net/?f=X_L%20%3D%20wL)
Substituting values
![X_L = 2.72 * 25*10^{-3}](https://tex.z-dn.net/?f=X_L%20%3D%202.72%20%2A%2025%2A10%5E%7B-3%7D)
![X_L =0.068](https://tex.z-dn.net/?f=X_L%20%3D0.068)
The impedance of the circuit is mathematically represented as
![z = \sqrt{(X_L -X_c) ^2 + (R)^2}](https://tex.z-dn.net/?f=z%20%3D%20%5Csqrt%7B%28X_L%20-X_c%29%20%5E2%20%2B%20%28R%29%5E2%7D)
Substituting values
![z = \sqrt{(0.068 - 0.068) ^2 + (90)^2}](https://tex.z-dn.net/?f=z%20%3D%20%5Csqrt%7B%280.068%20-%200.068%29%20%5E2%20%2B%20%2890%29%5E2%7D)
![z = 90](https://tex.z-dn.net/?f=z%20%3D%2090)
The maximum current supplied to the circuit is
![I_{max} = \frac{E_o}{z}](https://tex.z-dn.net/?f=I_%7Bmax%7D%20%3D%20%5Cfrac%7BE_o%7D%7Bz%7D)
So ![I_{max} = \frac{180}{90}](https://tex.z-dn.net/?f=I_%7Bmax%7D%20%3D%20%5Cfrac%7B180%7D%7B90%7D)
=> ![I_{max} = 2A](https://tex.z-dn.net/?f=I_%7Bmax%7D%20%3D%20%202A)
Now the maximum voltage across the inductor is
![V_i = I_{max} * X_L](https://tex.z-dn.net/?f=V_i%20%3D%20I_%7Bmax%7D%20%2A%20X_L)
So ![V_i =2 * 0.068](https://tex.z-dn.net/?f=V_i%20%3D2%20%2A%200.068)
=> ![V_i = 0.136 V](https://tex.z-dn.net/?f=V_i%20%3D%200.136%20V)