A 120-V rms voltage at 60.0 Hz is applied across an inductor, capacitor and a 100-Ω resistor in
series. If the maximum value of the current in this circuit is 1.60 A, what is the rms value of the
current in this circuit?
To find the rms value of the current in this circuit, we need to calculate the current using the given information.
1. First, find the peak voltage using the given rms voltage:
The peak voltage (Vp) can be found by multiplying the rms voltage (Vrms) by the square root of 2 (sqrt(2)) as follows:
Vp = Vrms * sqrt(2)
Vp = 120 V * sqrt(2)
2. Calculate the peak current using the maximum value of the current:
The peak current (Ip) can be found by dividing the maximum current (Imax) by the square root of 2 (sqrt(2)) as follows:
Ip = Imax / sqrt(2)
Ip = 1.60 A / sqrt(2)
3. Now that we have both the peak voltage and peak current, we can calculate the impedance of the series circuit. The impedance (Z) is given by:
Z = Vp / Ip
Z = (120 V * sqrt(2)) / (1.60 A / sqrt(2))
4. Finally, calculate the rms value of the current using Ohm's Law:
The rms current (Irms) can be found by dividing the peak voltage by the impedance as follows:
Irms = Vrms / Z
Irms = 120 V / Z
By following these steps, you can calculate the rms value of the current in the circuit.
To find the rms value of the current in this circuit, we need to use the relationship between the maximum value of the current (I_max) and the rms value of the current (I_rms).
The relationship is given by:
I_rms = I_max / √2
Where:
I_rms is the rms value of the current
I_max is the maximum value of the current
In this case, we are given that the maximum value of the current is 1.60 A.
Plugging this value into the formula, we get:
I_rms = 1.60 A / √2
To solve this, we need to calculate the square root of 2, and then divide 1.60 A by that value.
Using a calculator, the square root of 2 is approximately 1.414.
Now we can calculate the rms value of the current:
I_rms = 1.60 A / 1.414
I_rms ≈ 1.13 A
Therefore, the rms value of the current in this circuit is approximately 1.13 A.