JEE Advanced · Physics · 22. AC Circuits

A series $R$ - $C$ circuit is connected to $A C$ 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 $I_R^A>I_R^B$
B $I_R^A < I_R^B$
C $V_C^A>V_C^B$
D $V_C^A < V_C^B$

Verified Solution

Answer & Solution

Correct Answer

(C) $V_C^A>V_C^B$

Step-by-step Solution

Detailed explanation

$Z=\sqrt{R^2+X_C^2}=\sqrt{R^2+\left(\frac{1}{\omega C}\right)^2}$
In case (b) capacitance $C$ will be more.
Therefore, impedance $Z$ will be less.
Hence, current will be more.
$\therefore$ Option (b) is correct.
Further, $\quad \begin{aligned} V_C & =\sqrt{V^2-V_R^2} \\ & =\sqrt{V^2-(I R)^2}\end{aligned}$
In case (b), since current $I$ is more.
Therefore, $V_C$ will be less.
$\therefore$ Option (c) is correct.
$\therefore$ Correct options are (b) and (c).
Analysis of Question
(i) Question is moderately difficult.
(ii) In my opinion problems of alternating currents are not very difficult.
(iii) Topic of $A C$ is small. One can feel comfortable in this topic by putting less efforts.

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Answer the following by appropriately matching the lists based on the information given in the paragraph.
In a thermodynamics process on an ideal monatomic gas, the infinitesimal heat absorbed by the gas is given by

T Δ X,

where

T

is temperature of the system and

Δ X

is the infinitesimal change in a thermodynamic quantity

X

of the system. For a mole of monatomic ideal gas

X = \frac{3}{2} R l n (\frac{T}{T_{A}}) + R l n (\frac{V}{V_{A}}) .

Here,

R

is gas constant,

V

is volume of gas,

T_{A}

and

V_{A}

are constants.
The List-I below gives some quantities involved in a process and List-II gives some possible values of these quantities.

	Column - I		Column - II
(a)	Work done by the system in process $1 \to 2 \to 3$	(p)	$\frac{1}{3} R T_{0} l n 2$
(b)	Change in internal energy in process $1 \to 2 \to 3$	(q)	$\frac{1}{3} R T_{0}$
(c)	Heat absorbed by the system in process $1 \to 2 \to 3$	(r)	$R T_{0}$
(d)	Heat absorbed by the system in process $1 \to 2$	(s)	$\frac{4}{3} R T_{0}$
		(t)	$\frac{1}{3} R T_{0} (3 + l n 2)$
		(u)	$\frac{5}{6} R T_{0}$

If the process on one mole of monatomic ideal gas is as shown in the

P V

-diagram with

P_{0} V_{0} = \frac{1}{3} R T_{0},

the correct match is

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From JEE Advanced

Columns 1, 2 and 3 contain starting materials, reaction conditions and type of reactions respectively.

Column 1	Column 2	Column 3
(I) Toulene	(i) $NaOH$ $ /Br _2$	(P) Condensation
(II) Acetophenone	(ii) $B r_2 / h v$	(Q) Carboxylation
(III) Benzaldehyde	(iii) $\left( CH _3 CO \right)_2$ $O / CH _3$ $COOK$	(R) Substitution
(IV) Phenol	(iv) $NaOH$ $/CO _2$	(S) Haloform

For the synthesis of benzoic acid the only correct combination is

JEE Advanced 2017 Medium

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