Question

voltage across resistance inductance and capacitance connected in series are 3v, 4v and 5v. if supply voltage has 50hz frequency, what is the magnitude of supply voltage. find the resonant frequency of this series RLC circuit?​

Answer 1

Answer:

See the picture

Explanation:

Hope it helps you

Answer 2

Answer:

The supply voltage is found to be $2\sqrt{3}$ volts and the resonant frequency is $\frac{25}{\pi } Hz$

Explanation:

Here we have been given that the voltages across the given resistance inductance and also the capacitance all connected in series are 3V, 4V, and 5V

The voltage of the supply voltage (V) can be calculated by the following formula as below;

Let $V_{1}$ be the voltage of the resistance, $V_{2}$ be the voltage of the inductance and $V_{3}$ be the voltage of the capacitance then we have,

$V_{1} = 3V$

$V_{2} = 4V$

$V_{3} = 5V$

∴ V = $\sqrt{V_{1} ^{2} - (V_{3} -V_{2} )^{2} }$

⇒ V = $\sqrt{3^{2} - (5-4)^{2} }$

⇒ V = $\sqrt{9 - 1 }$

⇒ V = $\sqrt{8}$ volts

⇒ V = $2\sqrt{3}$ volts

Now the frequency of the supply voltage (f) is 50 Hz and we have to find the resonant frequency $(f_{r} )$ of the series RLC circuit. Therefore we use the formula as below:

$f_{r} =$ $\frac{f}{2\pi }$

⇒ $f_{r} = \frac{50}{2\pi }$ Hz

⇒ $f_{r} = \frac{25}{\pi } Hz$

Therefore the supply voltage is $2\sqrt{3}$ volts and the resonant frequency is $\frac{25}{\pi } Hz$