What is the peak to peak Voltage across a 10 kilo ohm resistor that dissipates 50 mW?
The rms voltage Vrms satisfies the equation
P = 50*10^-3 W = Vrms^2/R = V^2/50*10^3 ohms
Vrms^2 = 50^2
Vrms = 50 V
The peak to peak voltage is higher by a factor of sqrt2
V(p-p) = 70.7 V
Well, let me calculate that for you, but before I go any further, are you sure you want me to answer? I mean, talking about peak to peak voltage across a resistor might send some people into a deep slumber!
To find the peak-to-peak voltage across a resistor, we'll need to use the power formula and Ohm's law.
1. First, let's convert the power from milliwatts to watts:
50 mW = 0.05 W
2. Next, we'll use the power formula to find the voltage across the resistor.
Power (P) = Voltage (V) squared / Resistance (R)
Rearranging the formula, we have:
V^2 = P * R
Plugging in the values:
V^2 = 0.05 W * 10,000 Ω
V^2 = 500
3. Now, we can solve for the voltage (V):
V = square root(500)
Taking the square root, we get:
V ≈ 22.36 V
This is the peak voltage across the resistor.
4. Finally, to find the peak-to-peak voltage, we double the peak voltage:
Peak-to-peak voltage = 2 * peak voltage
Peak-to-peak voltage ≈ 2 * 22.36 V
Peak-to-peak voltage ≈ 44.72 V
Therefore, the peak-to-peak voltage across a 10 kilo ohm resistor dissipating 50 mW is approximately 44.72 V.
To find the peak to peak voltage across a resistor, you need to know the power dissipated by the resistor and its resistance.
In this case, the power dissipated by the resistor is given as 50 mW (milliwatts) and the resistance is 10 kilo ohms (10,000 ohms).
First, we need to convert the power to watts. Since 1 mW is equal to 0.001 watts, the power dissipated by the resistor is 0.05 watts.
Next, we can calculate the root mean square (RMS) voltage across the resistor using the formula:
Power (in watts) = (RMS voltage)^2 / Resistance
Plugging in the values, we can rearrange the formula to solve for the RMS voltage:
(RMS voltage)^2 = Power × Resistance
(RMS voltage)^2 = 0.05 watts × 10,000 ohms
(RMS voltage)^2 = 500 volts
Taking the square root of both sides, we find that the RMS voltage is the square root of 500 volts.
RMS voltage = √500 volts ≈ 22.36 volts
Finally, the peak to peak voltage is twice the RMS voltage:
Peak to peak voltage = 2 × RMS voltage
Peak to peak voltage = 2 × 22.36 volts ≈ 44.72 volts
Therefore, the peak to peak voltage across the 10 kilo ohm resistor that dissipates 50 mW is approximately 44.72 volts.