In a series circuit, a generator (1254 Hz, 13.8 V) is connected to a 15.5-Ω resistor, a 4.25-µF capacitor, and a 5.32-mH inductor. Find the voltage across each circuit element.
VR =
VC =
VL =
To find the voltage across each circuit element in a series circuit, you need to use Ohm's Law and the impedance formulas for capacitors and inductors.
1. Voltage across the resistor (VR):
Using Ohm's Law, we can calculate the voltage across the resistor using the formula: VR = I * R.
First, we need to calculate the current (I) flowing through the circuit. In a series circuit, the current is the same throughout.
Since we have a generator with a frequency (f) of 1254 Hz and voltage (V) of 13.8 V, we can use the formula for the impedance of a resistor (ZR) to calculate the current:
ZR = R
ZR = 15.5 Ω
To calculate the current (I):
I = V / ZR
I = 13.8 V / 15.5 Ω
Now that we have the current, we can calculate the voltage across the resistor:
VR = I * R
2. Voltage across the capacitor (VC):
The impedance of a capacitor (ZC) is given by the formula: ZC = 1 / (2πfC)
Given that the frequency (f) is 1254 Hz and the capacitance (C) is 4.25 µF, we can calculate the impedance of the capacitor:
ZC = 1 / (2π * 1254 Hz * 4.25 µF)
To calculate the current (I) flowing through the capacitor:
I = V / ZC
Now that we have the current, we can calculate the voltage across the capacitor:
VC = I * ZC
3. Voltage across the inductor (VL):
The impedance of an inductor (ZL) is given by the formula: ZL = 2πfL
Given that the frequency (f) is 1254 Hz and the inductance (L) is 5.32 mH, we can calculate the impedance of the inductor:
ZL = 2π * 1254 Hz * 5.32 mH
To calculate the current (I) flowing through the inductor:
I = V / ZL
Now that we have the current, we can calculate the voltage across the inductor:
VL = I * ZL
Using the appropriate formulas and calculations, you can find the voltage across each circuit element.