Question

When the key $K$ is pressed at time $t = 0$, then which of the following statements about the current $I$ in the resistor $AB$ of the given circuit is true?

A. At $t = 0$, $I = 2\,mA$ and with time it goes to $1\,mA$
B. $I$ oscillates between $1\,mA$ and $2\,mA$
C. $I = 2\,mA$ at all $t$
D. $I = 1\,mA$ at all $t$

Answer 1

Hint: We will use ohm’s law to calculate the current passing through the circuit in different time instances. The voltage or potential difference between two points in a circuit is directly proportional to the current and resistance, according to Ohm's law. $V = IR$ is the formula for Ohm's law.

Complete step by step answer:
We will observe that When k is pressed at $t = 0$ , the capacitor will begin to charge through the resistor between A and B, with no current flowing through the right resistor.Hence, when $t = 0$
$I = \dfrac{V}{R}$
It is given in the question that, $V = 2V$ and $R = 1000\Omega $
Substituting these values we get,
$I = \dfrac{2}{{1000}} = 2mA$

The charging will cease after a period of time, and current will pass through both resistors. The capacitor will be fully charged and in its stable state for some time. There will be no current passing through the capacitor now, and the circuit's effective resistance will be (1000+1000) = 2000.
Hence, $I = \dfrac{V}{R}$
We know that , $R = 2000\,\Omega $ and $V = 2\,V$
Substituting these values we get,
$ \therefore I = \dfrac{2}{{2000}} = 1\,mA$

Hence, the correct option is A.

Additional information:
While working with circuits, we must take the necessary precautions. When electricity is being supplied to a switch, we should not perform wiring. When electricity is being supplied, do not connect any of the charged terminals. When electricity is applied to a switch with insufficient wiring or soldering, irregular heating may occur, potentially resulting in burns.Hence, we must take preventative action.

Note: When current runs through the circuit, it is considered a 'closed circuit,' and when it does not, it is called a 'open circuit.' The switch or key assists in making or breaking the circuit, i.e. turning on or off the current. If there is not a switch in the circuit , the battery we are using would easily deplete. It aids in energy conservation.