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 lav between current maximum and voltage maximum?

Solution

Here given,
Capacitance, $C = 100 μF = 100 \times 10^{- 6} F = 10^{- 4} F$
Resistance, R = 40 Ω

$Rms voltage, E_{v} = 110 volt Peak voltage, E_{0} = \sqrt{2} . E_{v} = \sqrt{2} \times 110 V Frequency of Ac supply, v = 60 Hz ., ∴ ω = 2 πv = 120 π rad / s Peak current, I_{0} = ?$

a.) In RC circuit, as
$Z = \sqrt{R^{2} + X_{c}^{2}} = \sqrt{R^{2} + \frac{1}{ω^{2} C^{2}}}$
Therefore,

$I_{0} = \frac{E_{0}}{\sqrt{R^{2} + \frac{1}{ω^{2} C^{2}}}} = \frac{\sqrt{2} \times 110}{\sqrt{1600 + \frac{1}{{(120 π \times 10^{- 4})}^{2}}}}$
$I_{0} = 3.24 amp .$

b.) In RC circuit, voltage lags behind the current by phase angle ϕ,
where ϕ is given by,

$\tan ϕ = \frac{1 / ωC}{R} = \frac{1}{ωCR} = \frac{1}{120 π \times 10^{- 4} \times 40} = 0.6628$

$\Rightarrow ϕ = \tan^{- 1} (0.6628) = 33.5 ° = \frac{33.5 π}{180} rad .$
Hence,

$Time lag = \frac{ϕ}{ω} = \frac{33.5 π}{180 \times 120 π} = 1.55 \times 10^{- 3} \sec .$

For Daily Free Study Material Join wiredfaculty

Electrostatic Potential And Capacitance

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 lav between current maximum and voltage maximum?

Some More Questions From Electrostatic Potential and Capacitance Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction

For Daily Free Study Material Join wiredfaculty

Electrostatic Potential And Capacitance

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 lav between current maximum and voltage maximum?

Some More Questions From Electrostatic Potential and Capacitance Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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 lav between current maximum and voltage maximum?