In an LCR circuit, capacitance is changed from C to 2C. For the resonant frequency to remain unchanged, the inductance should be changed from L to

Question

In an LCR circuit, capacitance is changed from C to 2C. For the resonant frequency to remain unchanged, the inductance should be changed from L to (A) 4L (B) 2L (C) L/2 (D) L/4

Tardigrade Admin · Accepted Answer

In the condition of resonance XL=XC Or ω L=(1/ω C) ?.(i) Since, resonant frequency remains unchanged, so, √LC=constant or LC= constant ∴ L1C1=L2C2 ⇒ L× C=L2× 2C ⇒ L2=(L/2)

Q. In an LCR circuit, capacitance is changed from C to 2C. For the resonant frequency to remain unchanged, the inductance should be changed from L to

4L

2L

L/2

L/4

In the condition of resonance $X_{L} = X_{C}$ Or $ω L = \frac{1}{ω C}$ ?.(i) Since, resonant frequency remains unchanged, so, $L C = co n s t an t$ or $L C =$ constant $∴$ $L_{1} C_{1} = L_{2} C_{2}$ $\Rightarrow$ $L \times C = L_{2} \times 2 C$ $\Rightarrow$ $L_{2} = \frac{L}{2}$

Q. In an LCR circuit, capacitance is changed from C to 2C. For the resonant frequency to remain unchanged, the inductance should be changed from L to

4L

2L

L/2

L/4

In the condition of resonance XL​=XC​ Or ωL=ωC1​ ?.(i) Since, resonant frequency remains unchanged, so, LC​=constant or LC= constant ∴ L1​C1​=L2​C2​ ⇒ L×C=L2​×2C ⇒ L2​=2L​

In the condition of resonance $X_{L} = X_{C}$ Or $ω L = \frac{1}{ω C}$ ?.(i) Since, resonant frequency remains unchanged, so, $L C = co n s t an t$ or $L C =$ constant $∴$ $L_{1} C_{1} = L_{2} C_{2}$ $\Rightarrow$ $L \times C = L_{2} \times 2 C$ $\Rightarrow$ $L_{2} = \frac{L}{2}$