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An ac voltage has frequency of 50 Hz with peak amplitude of 100 V. In how many seconds after the zero value, voltage will attain the value of 86.6 V?
- a)1/300 second
- b)1/100 second
- c)1/150 second
- d)1/600 second
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
An ac voltage has frequency of 50 Hz with peak amplitude of 100 V. In ...
Given that, Vm = 100 V
V = 86.6 V
f = 50 ⇒ ω = 2πf = 100 π
V = Vm sin ωt
⇒ 86.6 = 100 sin (100 πt)
⇒ sin (100 πt) = 0.866
Most Upvoted Answer
An ac voltage has frequency of 50 Hz with peak amplitude of 100 V. In ...
Given data:
Frequency of ac voltage = 50 Hz
Peak amplitude = 100 V
Required voltage = 86.6 V
Calculation:
The ac voltage can be represented by the equation:
V(t) = V_m * sin(ωt)
Where:
V(t) = instantaneous voltage at time t
V_m = peak amplitude of the voltage
ω = angular frequency = 2πf
t = time
In this case, V_m = 100 V and f = 50 Hz, so ω = 2π * 50 = 100π rad/s.
We need to find the time at which the voltage attains the value of 86.6 V.
So, we can set up the equation:
86.6 = 100 * sin(100πt)
To solve this equation, we can rearrange it as:
sin(100πt) = 0.866
Using the inverse sine function, we can find the time:
sin^(-1)(sin(100πt)) = sin^(-1)(0.866)
100πt = sin^(-1)(0.866)
t = (sin^(-1)(0.866)) / (100π)
Now, we can calculate the value of t using a calculator:
t ≈ 0.01 seconds
Therefore, the voltage will attain the value of 86.6 V after approximately 0.01 seconds.
Answer:
The correct option is (A) 1/300 second.
Frequency of ac voltage = 50 Hz
Peak amplitude = 100 V
Required voltage = 86.6 V
Calculation:
The ac voltage can be represented by the equation:
V(t) = V_m * sin(ωt)
Where:
V(t) = instantaneous voltage at time t
V_m = peak amplitude of the voltage
ω = angular frequency = 2πf
t = time
In this case, V_m = 100 V and f = 50 Hz, so ω = 2π * 50 = 100π rad/s.
We need to find the time at which the voltage attains the value of 86.6 V.
So, we can set up the equation:
86.6 = 100 * sin(100πt)
To solve this equation, we can rearrange it as:
sin(100πt) = 0.866
Using the inverse sine function, we can find the time:
sin^(-1)(sin(100πt)) = sin^(-1)(0.866)
100πt = sin^(-1)(0.866)
t = (sin^(-1)(0.866)) / (100π)
Now, we can calculate the value of t using a calculator:
t ≈ 0.01 seconds
Therefore, the voltage will attain the value of 86.6 V after approximately 0.01 seconds.
Answer:
The correct option is (A) 1/300 second.
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An ac voltage has frequency of 50 Hz with peak amplitude of 100 V. In how many seconds after the zero value, voltage will attain the value of 86.6 V?a)1/300 secondb)1/100 secondc)1/150 secondd)1/600 secondCorrect answer is option 'A'. Can you explain this answer?
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