An 850 resistor, a 1.11 μF capacitor, and an 1.8 H inductor are connected in series across a 120 Hz AC source for which the maximum voltage is 170 V.
A) Calculate the impedance of the circuit.
Answer in units of k ohms
B) Calculate the maximum current delivered by the source.
Answer in units of mA
C) Calculate the phase angle between the current and voltage.
Answer in units of degrees
A) Calculate the impedance of the circuit.
Answer in units of k ohms
B) Calculate the maximum current delivered by the source.
Answer in units of mA
C) Calculate the phase angle between the current and voltage.
Answer in units of degrees
-
ZR = 850 Ω
ZC = 1/(jwc) = 1/(j*2π*120*1.11E-6) = -j1194.86 Ω
ZL = jwL = j*2π*120*1.8 = j1357.17
So...
Zeq = ZR + ZC + ZL = 850 Ω + j162.311Ω = **(0.85 + j0.162311) kΩ**
Current is V/Z, so:
I = (170)/(0.85 + j0.162311) = 192.962 - j36.8436 mA = 196.45 < -10.9107° mA
So from there, your max current is 196.45 mA. When I gave voltage a phase of zero, the phase of the current turned out to be -10.9107°. So the voltage leads the current by 10.9107°.
EDIT: For A, the impedance of a resistor is simply the given value. For a capacitor, it's 1/(jωC). Since ω = 2πf, you could also write ZC = 1/(j2πfC) if that helps. That would make ZL = j2πfC. Since they're in series, just add up the three values. You could also write it in polar form, where if:
Z = a + jb
Then:
|Z| = √(a² + b²) --> magnitude
θ = arctan(b/a) --> angle
EDIT2: Here's a graph if you doubt my math:
http://img254.imageshack.us/img254/1148/…
ZC = 1/(jwc) = 1/(j*2π*120*1.11E-6) = -j1194.86 Ω
ZL = jwL = j*2π*120*1.8 = j1357.17
So...
Zeq = ZR + ZC + ZL = 850 Ω + j162.311Ω = **(0.85 + j0.162311) kΩ**
Current is V/Z, so:
I = (170)/(0.85 + j0.162311) = 192.962 - j36.8436 mA = 196.45 < -10.9107° mA
So from there, your max current is 196.45 mA. When I gave voltage a phase of zero, the phase of the current turned out to be -10.9107°. So the voltage leads the current by 10.9107°.
EDIT: For A, the impedance of a resistor is simply the given value. For a capacitor, it's 1/(jωC). Since ω = 2πf, you could also write ZC = 1/(j2πfC) if that helps. That would make ZL = j2πfC. Since they're in series, just add up the three values. You could also write it in polar form, where if:
Z = a + jb
Then:
|Z| = √(a² + b²) --> magnitude
θ = arctan(b/a) --> angle
EDIT2: Here's a graph if you doubt my math:
http://img254.imageshack.us/img254/1148/…