Answer:
a. Zin = 41.25 - j 16.35 Ω
b. V₁ = 143. 6 e⁻ ¹¹ ⁴⁶
c. Pin = 216 w
d. PL = Pin = 216 w
e. Pg = 478.4 w , Pzg = 262.4 w
Explanation:
a.
Zin = Zo * [ ZL + j Zo Tan (βl) ] / [ Zo + j ZL Tan (βl) ]
βl = 2π / λ * 0.15 λ = 54 °
Zin = 50 * [ 75 + j 50 Tan (54) ] / [ 50 + j 75 Tan (54) ]
Zin = 41.25 - j 16.35 Ω
b.
I₁ = Vg / Zg + Zin ⇒ I₁ = 300 / 41.25 - j 16.35 = 3.24 e ¹⁰ ¹⁶
V₁ = I₁ * Zin = 3.24 e ¹⁰ ¹⁶ * ( 41.25 - j 16.35)
V₁ = 143. 6 e⁻ ¹¹ ⁴⁶
c.
Pin = ¹/₂ * Re * [V₁ * I₁]
Pin = ¹/₂ * 143.6 ⁻¹¹ ⁴⁶ * 3.24 e ⁻ ¹⁰ ¹⁶ = 143.6 * 3.24 / 2 * cos (21.62)
Pin = 216 w
d.
The power PL and Pin are the same as the line is lossless input to the line ends up in the load so
PL = Pin
PL = 216 w
e.
Pg Generator
Pg = ¹/₂ * Re * [ V₁ * I₁ ] = 486 * cos (10.16)
Pg = 478.4 w
Pzg dissipated
Pzg = ¹/₂ * I² * Zg = ¹/₂ * 3.24² * 50
Pzg = 262.4 w
Answer:
The Momentum Calculator uses the formula p=mv, or momentum (p) is equal to mass (m) times velocity (v). The calculator can use any two of the values to calculate the third.
Explanation:
Answer:
Fnet = 12 N
Explanation:
Force on a point charge due to another point charge = kq1q2 / d^2
Force on +32uC = due to + 20uC + due to -60uC
where uC = 1 x 10^-6 C and k = 9 x 10^9 N m^2 / C^2
Net Force =
![= \frac{1}{4\pi \epsilon _0} [\frac{32 \times 10^-^6 \times60\times10^-^6}{(60/100)^2}-\frac{32 \times 10^-^6 \times20\times10^-^6}{ (40/100)^2} ]](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B1%7D%7B4%5Cpi%20%5Cepsilon%20_0%7D%20%5B%5Cfrac%7B32%20%5Ctimes%2010%5E-%5E6%20%5Ctimes60%5Ctimes10%5E-%5E6%7D%7B%2860%2F100%29%5E2%7D-%5Cfrac%7B32%20%5Ctimes%2010%5E-%5E6%20%5Ctimes20%5Ctimes10%5E-%5E6%7D%7B%20%2840%2F100%29%5E2%7D%20%20%5D)
![F_{net}=9 \times10^9\times 10^-^1^2[\frac{32\times60\times10^4}{60\times60} -\frac{32\times20\times10^4}{40\times40} ]](https://tex.z-dn.net/?f=F_%7Bnet%7D%3D9%20%5Ctimes10%5E9%5Ctimes%2010%5E-%5E1%5E2%5B%5Cfrac%7B32%5Ctimes60%5Ctimes10%5E4%7D%7B60%5Ctimes60%7D%20-%5Cfrac%7B32%5Ctimes20%5Ctimes10%5E4%7D%7B40%5Ctimes40%7D%20%5D)
![=90[32(\frac{80-60}{60\times 80} )]\\\\=90\times32\times0.004167\\\\=12N](https://tex.z-dn.net/?f=%3D90%5B32%28%5Cfrac%7B80-60%7D%7B60%5Ctimes%2080%7D%20%29%5D%5C%5C%5C%5C%3D90%5Ctimes32%5Ctimes0.004167%5C%5C%5C%5C%3D12N)
Fnet = 12 N
