Advertisements
Advertisements
Question
A 100 µF capacitor in series with a 40 Ω resistance is connected to a 110 V, 60 Hz supply.
(a) What is the maximum current in the circuit?
(b) What is the time lag between the current maximum and the voltage maximum?
Advertisements
Solution
Capacitance of the capacitor, C = 100 μF = 100 × 10−6 F
Resistance of the resistor, R = 40 Ω
Supply voltage, V = 110 V
(a) Frequency of oscillations, v = 60 Hz
Angular frequency, ω = 2πv = 2π × 60 rad/s
For an RC circuit, we have the relation for impedance as:
Z = `"R"^2 + 1/(ω^2"C"^2)`
Peak voltage, V0 = `"V"sqrt2 = 110 sqrt2 "V"`
Maximum current is given as:
I0 = `"V"_0/"Z"`
= `"V"_0/sqrt("R"^2 + 1/(ω^2"C"^2))`
= `(110 sqrt2)/sqrt((40)^2 + 1/((120π)^2 xx (10^-4)^2))`
= `(110 sqrt2)/sqrt(1600 + 10^8/(120π)^2)`
= 3.24 A
(b) In a capacitor circuit, the voltage lags behind the current by a phase angle of Φ. This angle is given by the relation:
∴ `tan phi = (1/(ω"C"))/"R" = 1/(ω"CR")`
= `1/(120π xx 10^-4 xx 10)`
= 0.6635
`phi` = tan−1 (0.6635) = 33.56°
= `(33.56π)/180 "rad"`
∴ Time lag = `phi/ω`
= `(33.56π)/(180 xx 120π)`
= 1.55 × 10−3 s
= 1.55 ms
Hence, the time lag between maximum current and maximum voltage is 1.55 ms.
APPEARS IN
RELATED QUESTIONS
The magnetic field energy in an inductor changes from maximum to minimum value in 5.0 ms when connected to an AC source. The frequency of the source is
An inductor, a resistance and a capacitor are joined in series with an AC source. As the frequency of the source is slightly increased from a very low value, the reactance
An inductor coil of some resistance is connected to an AC source. Which of the following quantities have zero average value over a cycle?
(a) Current
(b) Induced emf in the inductor
(c) Joule heat
(d) Magnetic energy stored in the inductor
A 44 mH inductor is connected to 220 V, 50 Hz ac supply. Determine the rms value of the current in the circuit.
Obtain if the circuit is connected to a 110 V, 12 kHz supply? Hence, explain the statement that a capacitor is a conductor at very high frequencies. Compare this behaviour with that of a capacitor in a dc circuit after the steady state.
An applied voltage signal consists of a superposition of a dc voltage and an ac voltage of high frequency. The circuit consists of an inductor and a capacitor in series. Show that the dc signal will appear across C and the ac signal across L.
Alternating current is so called because _______.
In a circuit containing resistance only, voltage and current are ______.
Explain why the reactance offered by an inductor increases with increasing frequency of an alternating voltage.
An electrical device draws 2kW power from AC mains (voltage 223V (rms) = `sqrt(50,000)` V). The current differs (lags) in phase by `phi(tan phi = (-3)/4)` as compared to voltage. Find (i) R, (ii) XC – XL, and (iii) IM. Another device has twice the values for R, XC and XL. How are the answers affected?
An ac voltage V = V0 sin ωt is applied across a pure inductor of inductance L. Find an expression for the current i, flowing in the circuit and show mathematically that the current flowing through it lags behind the applied voltage by a phase angle of `π/2`. Also draw graphs of V and i versus ωt for the circuit.
An ideal inductor is connected across an AC source of voltage. The current in the circuit ______.
In an AC circuit with a bulb and inductor, what happens to the bulb’s brightness when an iron rod is inserted into the inductor?
The magnetic potential energy stored in a certain inductor is 25 mJ, when the current in the inductor is 60 mA. This inductor is of inductance ______.
A 2 mH inductor is connected to 220 V, 50 Hz AC (X1) and then to DC (X2). Find X1 and X2.
A series LCR circuit is subjected to an AC signal of 200 V, 50 Hz. If the voltage across the inductor (L = 10 mH) is 31.4 V, then the current in this circuit is ______.
