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In LCR series circuit source voltage is ...

In LCR series circuit source voltage is 120 volt and voltage in inductor 50 volt and resistance is 40 volt then determine voltage in capacitor.

A

`V_(C) = 10(5-8sqrt(2))`

B

`V_(C) = 10(5+8sqrt(2))`

C

`V_(C) = 20(5+8sqrt(2))`

D

`V_(C) = 10(5+7sqrt(2))`

Text Solution

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The correct Answer is:
To solve the problem step by step, we can use the relationship between the voltages in an LCR series circuit. The total voltage in the circuit is equal to the vector sum of the voltages across the resistor (Vr), inductor (Vl), and capacitor (Vc). ### Step 1: Understand the relationship In an LCR series circuit, the source voltage (Vs) is given by: \[ V_s = V_r + V_l - V_c \] Where: - \( V_s \) = Source voltage - \( V_r \) = Voltage across the resistor - \( V_l \) = Voltage across the inductor - \( V_c \) = Voltage across the capacitor ### Step 2: Substitute the known values From the problem, we know: - \( V_s = 120 \, V \) - \( V_l = 50 \, V \) - \( V_r = 40 \, V \) Substituting these values into the equation: \[ 120 = 40 + 50 - V_c \] ### Step 3: Simplify the equation Now, simplify the equation: \[ 120 = 90 - V_c \] ### Step 4: Solve for Vc Rearranging the equation to solve for \( V_c \): \[ V_c = 90 - 120 \] \[ V_c = -30 \, V \] ### Step 5: Interpret the result The negative sign indicates that the voltage across the capacitor is 30 volts, but it is opposite in phase to the voltage across the inductor. ### Final Answer The voltage across the capacitor \( V_c \) is \( 30 \, V \). ---
To solve the problem step by step, we can use the relationship between the voltages in an LCR series circuit. The total voltage in the circuit is equal to the vector sum of the voltages across the resistor (Vr), inductor (Vl), and capacitor (Vc). ### Step 1: Understand the relationship In an LCR series circuit, the source voltage (Vs) is given by: \[ V_s = V_r + V_l - V_c \] Where: - \( V_s \) = Source voltage - \( V_r \) = Voltage across the resistor ...
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