Question 717: Current Electricity

Question

In the circuit shown below, the key is pressed at time t = 0. Which of the following statement(s) is (are) true?

Accepted Answer

When the key is just pressed, there is no charge on capacitors
$$	herefore$$ $$5 = 25000{I_1} \Rightarrow {I_1} = {5 \over {25000}} = 0.2\,mA$$
and $$5 = 50000{I_2} \Rightarrow {I_2} = {5 \over {50000}} = 0.1\,mA$$
Reading of voltmeter $$ = {V_Q} - {V_P} =  - 25000{I_1}$$
$$ =  - 25000 	imes 0.2 	imes {10^{ - 3}}V =  - 5V$$
After a very long time, steady state is reached, i.e. $${I_1} - {I_2} = 0$$
$$	herefore$$ $$5 = {{{q_1}} \over {40 	imes {{10}^{ - 6}}}}$$ or $${q_1} = 200\mu C$$
and $$	herefore$$ $$5 = {{{q_2}} \over {20 	imes {{10}^{ - 6}}}}$$ or $${q_2} = 100\mu C$$
Now, reading of voltmeter $$ = {V_Q} - {V_P}$$
$$ = {{{q_2}} \over {20\mu F}} = {{100\mu C} \over {20\mu F}} = 5V$$
For capacitor of 40$$\mu$$F,
$${	au _1} = RC = 25 	imes {10^3} 	imes 40 	imes {10^{ - 6}} = 1\,s$$
and for capacitor of 20$$\mu$$F,
$${	au _2} = RC = 50 	imes {10^3} 	imes 20 	imes {10^{ - 6}} = 1\,s$$
$$	herefore$$ At any instant t,
$${q_1} = 200[1 - {e^{ - t}}]\mu C$$, $${q_2} = 100[1 - {e^{ - t}}]\mu C$$
$${I_1} = 0.2\,{e^{ - t}}$$ mA, $${I_2} = 0.1\,{e^{ - t}}$$ mA
$${V_Q} - {V_P} = {{100(1 - {e^{ - t}})\mu C} \over {20\mu F}} - 25k\Omega  	imes 0.2\,{e^{ - t}}$$ mA
$$ = 5(1 - {e^{ - t}}) - 5{e^{ - t}} = 5 - 10{e^{ - t}}$$
At t = ln 2 s; $${V_Q} - {V_P} = 5 - 10{e^{ - \ln 2}} = 5 - {{10} \over 2} = 0$$ V
Initially, I
0
= 0.1 mA + 0.2 mA = 0.3 mA
At t = 1 s, I = I
1
+ I
2
$$ = (0.2{e^{ - 1}} + 0.1{e^{ - 1}}) = {{0.3} \over e}\,mA = {{{I_0}} \over e}$$
After a long time, i.e. t $$	o$$ $$\infty$$
$$I = {I_1} + {I_2} = 0.2{e^{ - \infty }} + 0.1{e^{ - \infty }} = 0$$

Answer

The voltmeter display $$-$$5V as soon as the key is pressed and displays +5 V after a long time

Answer

The voltmeter will display 0 V at time t = ln 2 seconds

Answer

The current in the ammeter becomes 1/e of the initial value after 1 second

Answer

The current in the ammeter becomes zero after a long time

Current Electricity

In the circuit shown below, the key is pressed at time t = 0. Which of the following statement(s) is (are) true?

Choose the correct answer: