An inductor L in series with a resistor R , driven by a sinusoidal voltage source, responds as described by the following differential equation: V 0 sin ω t = L d I d t + R I . Show that a current of the form I = I 0 sin ( ω t − ϕ ) flows through the circuit by direct substitution into the differential equation. Determine the amplitude of the current ( I 0 ) and the phase difference ϕ between the current and the voltage source.
An inductor L in series with a resistor R , driven by a sinusoidal voltage source, responds as described by the following differential equation: V 0 sin ω t = L d I d t + R I . Show that a current of the form I = I 0 sin ( ω t − ϕ ) flows through the circuit by direct substitution into the differential equation. Determine the amplitude of the current ( I 0 ) and the phase difference ϕ between the current and the voltage source.
An inductor L in series with a resistor R, driven by a sinusoidal voltage source, responds as described by the following differential equation:
V
0
sin
ω
t
=
L
d
I
d
t
+
R
I
.
Show that a current of the form
I
=
I
0
sin
(
ω
t
−
ϕ
)
flows through the circuit by direct substitution into the differential equation. Determine the amplitude of the current (I0) and the phase difference ϕ between the current and the voltage source.
A resistor (R = 1 Ω), inductor (L = 0.1 H) and capacitor (C = 0.1 F) are connected in series, and the current I(t) through the circuit is measured as shown in the image below
Assuming that the capacitor is uncharged at t = 0, and that the circuit is electrically small (such that propagation times between components can be neglected), find (or approximate where necessary) for times t = [0 : 0.1 : 0.4] (i.e. do not calculate at t = 0.5):
1) The voltage VR(t) across the resistor, where VR(t) = I(t) · R.
A 200 Ω resistor, 1.6 H inductor, and 3.0 μF capacitor are connected in series across a 60 Hz, 120 V power supply. Calculate (a) the inductive reactance of the circuit, (b) its capacitive reactance, (c) its impedance, (d) the current through the circuit, and (e) the phase angle.
A resistor (R = 9.00 x 102 Ω), a capacitor (C 5 0.250 µF),and an inductor (L = 2.50 H) are connected in series across a2.40 x 102 - Hz AC source for which ΔVmax = 1.40 x 102 V.Calculate (a) the impedance of the circuit, (b) the maximumcurrent delivered by the source, and (c) the phase anglebetween the current and voltage. (d) Is the current leadingor lagging the voltage?
Chapter 30 Solutions
Modified Mastering Physics with Pearson eText -- Standalone Access Card -- for Physics for Scientists & Engineers with Modern Physics
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