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A sereis R-C circuit is connected to AC voltage source. Consider two cases, (A) when C is without a dielectric medium and (B) when C is filled with dielectric of constant 4. The current `I_(R)` through the resistor and voltage `V_(c)` across the capacitor are compared in the two cases. Which of the following is/ are true?A. `I_(R )^(B) gt I_(R )^(B)`B. `I_(R )^(B) = I_(R )^(B)`C. `V_(A)^(C ) gt V_(c )^(B)`D. `V_(A)^(C ) lt V_(c )^(B)` |
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Answer» Correct Answer - C For circuit `A`, Impedance, `Z_(A) = sqrt(R^(2) + (1)/(omega^(2) C^(2)))` Current in circuit, `I_(A)^(2) = (V)/(sqrt(R^(2) + (1)/(omega^(2) C^(2)))` Pot. Diff. across `C`, `V_(C )^(A) = I_(R)^(A) xx (1)/(omega C) = (V)/(sqrt((R omega C)^(2) + 1)` For circuit `B`, impedance ` Z_(B) = sqrt(R^(2) + (1)/((4 omega)^(2) C^(2)))` Current in circuit, `I_(B)^(B) = (V)/(sqrt(R^(2) + (1)/((4 omega)^(2) C^(2)))` Pot. diff. across `C`, `V_(C )^(B) = I_(R )^(B) xx (1)/( 4 omega C) = (V)/(sqrt((4 R omega C)^(2) + 1))` We conclude, form (i) and (iii) , `I_(R )^(B) gt I_(R )^(A)` From (ii) and (iv), `V_(C )^(A) gt V_(C )^(B)` choice (c ) is correct |
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