1
JEE Advanced 2023 Paper 1 Online
+3
-1
A series LCR circuit is connected to a $45 \sin (\omega t)$ Volt source. The resonant angular frequency of the circuit is $10^5 ~\mathrm{rad}~ \mathrm{s}^{-1}$ and current amplitude at resonance is $I_0$. When the angular frequency of the source is $\omega=8 \times 10^4 ~\mathrm{rad} ~\mathrm{s}^{-1}$, the current amplitude in the circuit is $0.05 I_0$. If $L=50 ~\mathrm{mH}$, match each entry in List-I with an appropriate value from List-II and choose the correct option.

List - I List - II
(P) $I_0$ in $\mathrm{mA}$ (1) 44.4
(Q) The quality factor of the circuit (2) 18
(R) The bandwidth of the circuit in $\mathrm{rad}~ \mathrm{s}^{-1}$ (3) 400
(S) The peak power dissipated at resonance in Watt (4) 2250
(5) 500
A
$P \rightarrow 2, Q \rightarrow 3, R \rightarrow 5, S \rightarrow 1$
B
$P \rightarrow 3, Q \rightarrow 1, R \rightarrow 4, S \rightarrow 2$
C
$P \rightarrow 4, Q \rightarrow 5, R \rightarrow 3, S \rightarrow 1$
D
$P \rightarrow 4, Q \rightarrow 2, R \rightarrow 1, S \rightarrow 5$
2
JEE Advanced 2017 Paper 2 Offline
+3
-0
Consider a simple RC circuit as shown in Figure 1.

Process 1 : In the circuit the switch S is closed at t = 0 and the capacitor is fully charged to voltage V0 (i.e. charging continues for time T >> RC). In the process some dissipation (ED) occurs across the resistance R. The amount of energy finally stored in the fully charged capacitor is EC.

Process 2 : In a different process the voltage is first set to $${{{V_0}} \over 3}$$ and maintained for a charging time T >> RC. Then, the voltage is raised to $${{2{V_0}} \over 3}$$ without discharging the capacitor and again maintained for a time T >> RC. The process is repeated one more time by raising the voltage to V0 and the capacitor is charged to the same final voltage V0 as in Process 1.

These two processes are depicted in Figure 2. In Process 1, the energy stored in the capacitor EC and heat dissipated across resistance ED are related by
A
EC = ED ln2
B
EC = ED
C
EC = 2ED
D
EC = $${1 \over 2}$$ED
3
JEE Advanced 2017 Paper 2 Offline
+3
-0
Consider a simple RC circuit as shown in Figure 1.

Process 1 : In the circuit the switch S is closed at t = 0 and the capacitor is fully charged to voltage V0 (i.e. charging continues for time T >> RC). In the process some dissipation (ED) occurs across the resistance R. The amount of energy finally stored in the fully charged capacitor is EC.

Process 2 : In a different process the voltage is first set to $${{{V_0}} \over 3}$$ and maintained for a charging time T >> RC. Then, the voltage is raised to $${{2{V_0}} \over 3}$$ without discharging the capacitor and again maintained for a time T >> RC. The process is repeated one more time by raising the voltage to V0 and the capacitor is charged to the same final voltage V0 as in Process 1.

These two processes are depicted in Figure 2. In Process 2, total energy dissipated across the resistance ED is
A
$${E_D} = {1 \over 3}\left( {{1 \over 2}CV_0^2} \right)$$
B
$${E_D} = 3\left( {{1 \over 2}CV_0^2} \right)$$
C
$${E_D} = 3CV_0^2$$
D
$${E_D} = {1 \over 2}CV_0^2$$
4
IIT-JEE 2010 Paper 1 Offline
+3
-1

An AC voltage source of variable angular frequency $$\omega$$ and fixed amplitude V0 is connected in series with a capacitance C and an electric bulb of resistance R (inductance zero). When $$\omega$$ is increased

A
the bulb glows dimmer.
B
the bulb glows brighter.
C
total impedance of the circuit is unchanged.
D
total impedance of the circuit increases.
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