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The voltage across and current through a circuit element are, respectively given as,
v(t) = 60 cos(100t + 40°) V
i(t) = 15 cos(100t − 20°) A
The power (in W) absorbed by the element is
(Answer up to the nearest integer)
Correct answer is '225'. Can you explain this answer?
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The voltage across and current through a circuit element are, respect...
Given Data:
Voltage across the circuit element: v(t) = 60 cos(100t - 40°) V
Current through the circuit element: i(t) = 15 cos(100t - 20°) A
Definition:
The power absorbed by a circuit element can be calculated using the formula P = VI, where P is the power in watts, V is the voltage in volts, and I is the current in amperes.
Calculating Power:
To calculate the power absorbed by the circuit element, we need to find the product of the instantaneous voltage and current at any given time.
The instantaneous voltage v(t) can be written as Vm * cos(ωt + φv), where Vm is the maximum voltage, ω is the angular frequency, t is the time, and φv is the phase angle of the voltage.
Similarly, the instantaneous current i(t) can be written as Im * cos(ωt + φi), where Im is the maximum current, ω is the angular frequency, t is the time, and φi is the phase angle of the current.
Since both voltage and current have the same angular frequency (ω), we can calculate the power absorbed by the circuit element using the formula:
P = Vm * Im * cos(φv - φi)
Calculating the power:
Given that v(t) = 60 cos(100t - 40°) V and i(t) = 15 cos(100t - 20°) A, we can determine the maximum voltage Vm = 60 V and the maximum current Im = 15 A.
The phase angle of the voltage φv = -40° and the phase angle of the current φi = -20°.
Using the formula for power, we substitute the given values:
P = 60 * 15 * cos(-40° - (-20°))
Simplifying the expression:
P = 900 * cos(-40° + 20°)
P = 900 * cos(-20°)
Using a calculator or table, we find that cos(-20°) ≈ 0.9397.
P ≈ 900 * 0.9397
P ≈ 845.73
Rounding the answer to the nearest integer, we get:
P ≈ 846 W
Therefore, the power absorbed by the circuit element is approximately 846 watts.
Voltage across the circuit element: v(t) = 60 cos(100t - 40°) V
Current through the circuit element: i(t) = 15 cos(100t - 20°) A
Definition:
The power absorbed by a circuit element can be calculated using the formula P = VI, where P is the power in watts, V is the voltage in volts, and I is the current in amperes.
Calculating Power:
To calculate the power absorbed by the circuit element, we need to find the product of the instantaneous voltage and current at any given time.
The instantaneous voltage v(t) can be written as Vm * cos(ωt + φv), where Vm is the maximum voltage, ω is the angular frequency, t is the time, and φv is the phase angle of the voltage.
Similarly, the instantaneous current i(t) can be written as Im * cos(ωt + φi), where Im is the maximum current, ω is the angular frequency, t is the time, and φi is the phase angle of the current.
Since both voltage and current have the same angular frequency (ω), we can calculate the power absorbed by the circuit element using the formula:
P = Vm * Im * cos(φv - φi)
Calculating the power:
Given that v(t) = 60 cos(100t - 40°) V and i(t) = 15 cos(100t - 20°) A, we can determine the maximum voltage Vm = 60 V and the maximum current Im = 15 A.
The phase angle of the voltage φv = -40° and the phase angle of the current φi = -20°.
Using the formula for power, we substitute the given values:
P = 60 * 15 * cos(-40° - (-20°))
Simplifying the expression:
P = 900 * cos(-40° + 20°)
P = 900 * cos(-20°)
Using a calculator or table, we find that cos(-20°) ≈ 0.9397.
P ≈ 900 * 0.9397
P ≈ 845.73
Rounding the answer to the nearest integer, we get:
P ≈ 846 W
Therefore, the power absorbed by the circuit element is approximately 846 watts.
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Community Answer
The voltage across and current through a circuit element are, respect...
V = 60∠40o V, I = 15∠-20oA
P = 1/2|V||I|cosθ
= 1/2(60)(15)cos60o
θ = 40o + 20o = 60o
= 1/2(60)(15) x 1/2 = 225 W
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The voltage across and current through a circuit element are, respectively given as,v(t) = 60 cos(100t + 40°) Vi(t) = 15 cos(100t − 20°) AThe power (in W) absorbed by the element is(Answer up to the nearest integer)Correct answer is '225'. Can you explain this answer?
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