1
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
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 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
$${E_D} = {1 \over 2}CV_0^2$$
3
IIT-JEE 2012 Paper 2 Offline
+4
-1
In the given circuit, a charge of $$+80$$ $$\mu C$$ is given to the upper plate of the $$4$$ $$\mu F$$ capacitor. Then in the steady state, the charge on the upper plate of the $$3$$ $$\mu F$$ capacitor is
A
$$+ \,32\,\mu C$$
B
$$+ \,40\,\mu C$$
C
$$+ \,48\,\mu C$$
D
$$+ \,80\,\mu C$$
4
IIT-JEE 2011 Paper 1 Offline
+2
-0.5
A $$2$$ $$\mu F$$ capacitor is charged as shown in the figure. The percentage of its stored energy dissipated after the switch $$S$$ is turned to position $$2$$ is
A
$$0\%$$
B
$$20\%$$
C
$$75\%$$
D
$$80\%$$
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