Question

In an L-C-R circuit, the values of R, $X_L$, and $X_C$ are 120Ω, 180Ω, and 130Ω. What is the impedance of the circuit?

Answer 1

Hint: As we all know that the impedance of the circuit is the resistance offered to the circuit for the flow of current to the circuit. It depends on both inductance and capacitive reactance. There are collisions taking place between charged particles and the structure of the internal components of the conductor.

Formula Used:
The formula for calculating the impedance of the circuit is:
$Z = \sqrt {{R^2} + {{\left( {{X_L} - {X_C}} \right)}^2}} $

Complete step by step solution:
Given: $R = 120\Omega $ , ${X_L} = 180\Omega $ and ${X_C} = 130\Omega $ .
The formula for calculating the impedance of the circuit is:
$Z = \sqrt {{R^2} + {{\left( {{X_L} - {X_C}} \right)}^2}} $
Here, $Z$ is the impedance, $R$ is the resistance, $X_L$ is the inductive reactance and $X_C$ is the capacitive reactance.
 Put the value of resistance, the inductive impedance, and the capacitive impedance in the above equation.
$Z = \sqrt {{{\left( {120} \right)}^2} + {{\left( {180 - 130} \right)}^2}} $
$ = \sqrt {{{\left( {130} \right)}^2}} $
$ = 130\,\Omega $

Therefore, the value of impedance is 130 ohms.

Note:
In voltmeter and oscilloscopes, we use high impedance circuits. High impedance means that a node in a circuit offers very little value of current per unit applied voltage at that point of time. Our headphones work on higher impedance levels to deliver high voltage.