Deck 7: Alternating Current, and Series A.C Circuits

Question 1

The current i through a resistor of pure resistance 2 kΩ varies with time t according to the equation i = 5 sin (2π x 100t + 45º) mA. The voltage across the resistor will thus be:

A) v = 5 sin (2 π % 100t + 45º) V
B) v = 5 sin (2 π % 100t - 45º) V
C) v = 10 sin (2 π % 100t + 45º) V
D) v = 10 sin (2 π % 100t + 135º) V

Answer 1

C

Question 2

The voltage v across a 1 μF pure capacitor varies with time t according to the equation v = 16 sin 2000t V. The current through the capacitor will thus be:

A) i = 16 sin 2000t mA
B) i = 16 sin (2000t + 90º) mA
C) i = 32 sin 2000t mA
D) i = 32 sin (2000t + 90º) mA

Answer 2

D

Question 3

The voltage v across a 4 H pure inductor varies with time t according to the equation v = 18 sin (2π x
1000t - 30º) V. The current through the capacitor will thus be:

A) i = 18 sin (2π x 1000t - 30º) mA
B) i = 18 sin (2π x 1000t - 120º) mA
C) i = 0.72 sin (2π x 1000t - 30º) mA
D) i = 0.72 sin (2π x 1000t - 120º) mA

Answer 3

D

Question 4

Decide whether each of these statements is True (T) or False
For alternating current with pure components, doubling the frequency:
(i) Doubles the reactance of an inductor.
(ii) Doubles the reactance of a capacitor.

A) (i) T (ii) T
B) (i) T (ii) F
C) (i) F (ii) T
D) (i) F (ii) F

Question 5

A circuit has a 300 Ω resistor in series with a 200 mH inductor. When a voltage v = 17 sin 2000t V is
Applied to it, the impedance is:

A) 400 Ω at 53.1º lagging the current
B) 400 Ω at 90º lagging the current
C) 500 Ω at 53.1º lagging the current
D) 500 Ω at 90º lagging the current

Question 6

Decide whether each of these statements is True (T) or False
With a series RCL circuit, at resonance:
(i) The voltage phasor for the capacitor is oppositely directed and equal in size to that of the inductor.
(ii) The circuit impedance is equal to the value of the resistance.

A) (i) T (ii) T
B) (i) T (ii) F
C) (i) F (ii) T
D) (i) F (ii) F

Question 7

Decide whether each of these statements is True (T) or False
An alternating current i varies with time t and its variation is described by the equation i = sin 3141t.
(i) The frequency of the alternating current is 500 Hz.
(ii) The periodic time of the alternating current is 2 ms.

A) (i) T (ii) T
B) (i) T (ii) F
C) (i) F (ii) T
D) (i) F (ii) F

Question 8

Decide whether each of these statements is True (T) or False
An alternating current i varies with time t and its variation is described by the equation i = 2 sin 500t.
(i) The average current over a cycle is 2 A.
(ii) The root-mean-square current is 1.41 A.

A) (i) T (ii) T
B) (i) T (ii) F
C) (i) F (ii) T
D) (i) F (ii) F