Question

a) an inductor of 85 mH is connected in series with 100 Ω resistor. If a sinusoidal current of 25 mA at 50 Hz flows in the circuit, determine:
a) the voltage dropped across the inductor;
b) the voltage dropped across the resistor;
c) the impedance of the circuit;
d) the supply Voltage;
e) the phase angle.

b) A capacitor of 22 µF is connected in series with a 640 Ω resistor if a sinusoidal current of 12 mA at 50 Hz flows in the circuit, determine:
a) the voltage dropped across the capacitor;
b) the voltage dropped across the resistor;
c) the impedance of the circuit;
d) the supply v

Answer 1

e) the phase angle.

(c) A series circuit comprises of an inductor of 85 mH, a resistor of 220 Ω and a capacitor of 22 µF. If a sinusoidal current of 40 mA at 50 Hz flows in this circuit, determine:

a) the voltage developed across the inductor;
b) the voltage dropped across the capacitor
c) the voltage dropped across the resistor;
d) the impedance of the circuit; the supply voltage;
e) the phase angle.

Answer 2

Any help would be deeply appreciated.

Answer 3

a)
$$
\large{
i(t)=.025\sin 2\pi ft\\
=.025\sin 2\pi50 t\\
=.025\sin 100\pi t\\
v_L(t)=L\cfrac{d}{dt}i(t)=L(0.025\times100\pi)\cos (100\pi t)\\
=.085\times2.5\pi\cos (100\pi t)\\
\approx 0.67\cos (100\pi t)~Volts\\
}
$$
b)
$$
\large{
v_R(t)=i(t)R\\
=100\times.025\sin 2\pi ft\\
=2.5\times \sin 100\pi t~Volts\\
}
$$
c)
$$
\large{
Z(t)=\cfrac{v(t)}{i(t)}\\
=\cfrac{v_L(t)+v_R(t)}{.025\sin 100\pi t}
}
$$
Substitute values determined in parts a and b above
d)
$$
\large
v(t)=v_L(t)+v_R(t)
$$
e) Use trig identities to simplify \(v(t)\) and put into form: \(A\cos (\omega t+\phi)\).
Where \(\phi\) is the phase angle.

Next circuit is handled similarly but will require integration rather than differentiation.

Answer 4

Thank you ybarrap

Answer 5

you're welcome