Physics · Alternating Current
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The relation between an alternative current voltage source and time in international system units is:
V = 120 sin (100𝜋t) cos (100𝜋t) volt value of peak velocity and frequency will be respectively:-
- A
120 volt and 100 Hz
- B
120/√2 volt and 100 Hz
- C
60 volt and 200 Hz
- D
60 volt and 100 Hz
Explanation is given below.
This option is incorrect.
V=120sin(100πt)cos(100πt)V
We know: sin2𝜭=2sin𝜭cos𝜭
V= 60sin2(100πt)V
=60sin200πtV
Let's compare it with standard equation:
V=V0sinωt
Hence peak velocity V0 is= 60V.
ω=200π
We know frequency f=ω/2π
=200π/2π
=100Hz ans
This option is incorrect.
V=120sin(100πt)cos(100πt)V
We know: sin2𝜭=2sin𝜭cos𝜭
V= 60sin2(100πt)V
=60sin200πtV
Let's compare it with standard equation:
V=V0sinωt
Hence peak velocity V0 is= 60V.
ω=200π
We know frequency f=ω/2π
=200π/2π
=100Hz ans
This option is incorrect.
V=120sin(100πt)cos(100πt)V
We know: sin2𝜭=2sin𝜭cos𝜭
V= 60sin2(100πt)V
=60sin200πtV
Let's compare it with standard equation:
V=V0sinωt
Hence peak velocity V0 is= 60V.
ω=200π
We know frequency f=ω/2π
=200π/2π
=100Hz ans
V=120sin(100πt)cos(100πt)V
We know: sin2𝜭=2sin𝜭cos𝜭
V= 60sin2(100πt)V
=60sin200πtV
Let's compare it with standard equation:
V=V0sinωt
Hence peak velocity V0 is= 60V. ans
ω=200π
We know frequency f=ω/2π
=200π/2π
=100Hz ans
The answer C in the key is incorrect, it should be D
Tagged under Physics · Alternating Current · 2017