The relation between an ac voltage source and time in SI units is V= 120 sin(100 π t)cos(100 π t) V. The value of peak voltage and frequency will be respectively

Question

The relation between an ac voltage source and time in SI units is V= 120 sin(100 π t)cos(100 π t) V. The value of peak voltage and frequency will be respectively (A) 120 V and 100 Hz (B) (120/√2)V and 100 Hz (C) 60 V and 200 Hz (D) 60 V and 100 Hz

Tardigrade Admin · Accepted Answer

V= 120 sin(100π t)cos(100 π t) V = 60 sin(200 π t) V (∵ sin2θ = 2 sinθ cosθ) Compare it with standard equation, V = V0 sinω t We get, V0 = 60 V and ω=200π or 2π upsilon =200π or upsilon=100 Hz

Q. The relation between an ac voltage source and time in $S I$ units is $V = 120 s in (100 π t) cos (100 π t) V$ .
The value of peak voltage and frequency will be respectively

$120 V$ and $100 Hz$

$\frac{120}{2} V$ and $100 Hz$

$60 V$ and $200 Hz$

$60 V$ and $100 Hz$

$V = 120 s in (100 π t) cos (100 π t) V$
$= 60 s in (200 π t) V (∵ s in 2 θ = 2 s in θ cos θ)$
Compare it with standard equation, $V = V_{0} s inω t$
We get, $V_{0} = 60 V$
and $ω = 200 π$ or $2 π υ = 200 π$ or $υ = 100 Hz$

Q. The relation between an ac voltage source and time in SI units is V=120sin(100πt)cos(100πt)V. The value of peak voltage and frequency will be respectively

120V and 100Hz

2​120​V and 100Hz

60V and 200Hz

60V and 100Hz