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In a series LCR circuit which is connect...

In a series LCR circuit which is connected to an AC vottage source, choose the incorrect statement

A

Algebraic sum of instantaneous vottage across L, C, R is a variable

B

`V_("Linst") + V_("Cinst") + V_("Rinst") = V_("Sourceinst")`

C

Vottage across inductor, capacitor, resistance behave as a vector

D

Current is same in inductor, capacitor and resistance

Text Solution

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The correct Answer is:
To solve the question regarding the incorrect statement in a series LCR circuit connected to an AC voltage source, we will analyze each option provided and determine which one is incorrect. ### Step-by-Step Solution: 1. **Understand the Circuit**: - A series LCR circuit consists of an inductor (L), a capacitor (C), and a resistor (R) connected in series to an AC voltage source. 2. **Analyze Option A**: - **Statement**: "The algebraic sum of instantaneous voltage across LCR is variable." - **Analysis**: In an LCR circuit, the instantaneous voltages across each component (inductor, capacitor, and resistor) change with time due to the alternating current. Therefore, the sum of these instantaneous voltages is indeed variable. - **Conclusion**: This statement is **true**. 3. **Analyze Option B**: - **Statement**: "The instantaneous voltage across inductor plus voltage drop across the capacitor and the voltage drop across the resistor is equal to the voltage source instantaneous." - **Analysis**: The correct relationship is given by the equation \( V = V_R + V_L - V_C \) (considering the phase differences). Thus, the sum of the voltages across the inductor and capacitor does not equal the source voltage instantaneously due to phase differences. - **Conclusion**: This statement is **false** (incorrect). 4. **Analyze Option C**: - **Statement**: "Voltage across inductor, capacitor, and resistor behaves as a vector." - **Analysis**: In AC circuits, voltages are represented as phasors (vectors) because they have both magnitude and phase. Therefore, this statement is **true**. 5. **Analyze Option D**: - **Statement**: "Current is the same in the inductor, capacitor, and resistance." - **Analysis**: In a series circuit, the same current flows through all components. Therefore, this statement is **true**. 6. **Final Conclusion**: - The incorrect statement is **Option B**: "The instantaneous voltage across inductor plus voltage drop across the capacitor and the voltage drop across the resistor is equal to the voltage source instantaneous." ### Summary: The incorrect statement in the series LCR circuit connected to an AC voltage source is Option B. ---
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