Q

# Help me please, When the rms voltages VL, VC and VR are measured respectively across the inductor L, the capacitor C and the resistor R in a series LCR circuit connected to an AC source, it is found that the ratio VL : VC : VR = 1 : 2 : 3. If the rms

When the rms voltages VL, VC and VR are  measured respectively across the inductor L, the capacitor C and the resistor R in a series  LCR  circuit  connected  to  an AC source, it is found that the ratio VL : VC : VR = 1 : 2 : 3. If the rms voltage of the AC source is 100 V, then VR is close to :

• Option 1)

50 V

• Option 2)

70 V

• Option 3)

90 V

• Option 4)

100 V

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$V_{R}=3K,\ V_{L}=K,\ V_{C}=2K$

$V=\sqrt{V_{R}^{2}+(V_{L}-V_{C})^{2}}$

or  $100V=\sqrt{9K^{2}+K^{2}}=K\sqrt{10}$

$\therefore V_{R}=3\times \frac{100}{\sqrt{10}}=94.86$

Option 1)

50 V

Incorrect

Option 2)

70 V

Incorrect

Option 3)

90 V

Correct

Option 4)

100 V

Incorrect

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