An rms voltage of 120 V produces a maximum current of 2.6 A in a certain resistor.Find the resistance of this resistor?
Imax = 2.6A = Peak value of the current.
Irms = 0.707 * 2.6 = 1.8382A.
R = Vrms / Irms = 120 / 1.8382 = 65.3
Ohms.
To find the resistance of the resistor, we can use Ohm's Law, which states that the resistance (R) is equal to the voltage (V) divided by the current (I).
Given that the root mean square (rms) voltage is 120 V and the maximum current is 2.6 A, we need to convert the rms voltage to the peak voltage.
The peak voltage (Vpeak) can be calculated by multiplying the rms voltage (Vrms) by the square root of 2 (sqrt(2)).
Vpeak = Vrms x sqrt(2)
= 120 V x sqrt(2)
≈ 120 V x 1.4142
≈ 169.7 V
Now we can use Ohm's Law to find the resistance:
R = Vpeak / I
= 169.7 V / 2.6 A
≈ 65.27 Ω
Therefore, the resistance of the resistor is approximately 65.27 ohms.
To find the resistance of the resistor, we can use Ohm's Law, which states that the resistance (R) is equal to the ratio of the voltage (V) across a resistor to the current (I) flowing through it.
Mathematically, Ohm's Law is expressed as:
R = V / I
In this case, we know that the RMS voltage (V) is 120 V and the maximum current (I) is 2.6 A.
We need to convert the maximum current to the RMS current since Ohm's Law requires the use of RMS values. In an AC circuit, the ratio of the RMS current to the maximum current depends on the waveform. For a sine wave, the RMS value is equal to the peak value divided by the square root of two.
RMS current, I_rms = I_max / √2
Substituting the given values, we can calculate the RMS current:
I_rms = 2.6 A / √2
I_rms ≈ 1.84 A
Now, we can calculate the resistance using Ohm's Law:
R = V / I_rms
R = 120 V / 1.84 A
R ≈ 65.22 Ω
Therefore, the resistance of the resistor is approximately 65.22 ohms.