Question

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

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

Answer 1

The Correct Option is B

To solve this problem, we need to analyze the behavior of the current in the resistor AB when the key K is pressed at time \( t = 0 \). This is a typical problem involving the time-dependent response of a circuit, possibly including components like resistors, capacitors, or inductors. The correct choice, according to the given answer, is: "at \( t = 0 \), \( I = 2 \, \text{mA} \) and with time it goes to \( 1 \, \text{mA} \)." Let's break down the reasoning:

1. When the key K is pressed, it implies an initial condition in the circuit where power is being applied, usually resulting in a sudden change or spike in current or voltage due to circuit elements trying to establish their steady state.
2. Initial Current at \( t = 0 \): At the very moment \( t = 0 \), circuits often have initial (almost instantaneous) conditions calculated by considering the short-circuited behavior of capacitors or the open-circuit behavior of inductors.
   • If it's determined that at \( t = 0 \), \( I = 2 \, \text{mA} \), it typically indicates the initial surge current the circuit faces when a key or switch is activated.
3. Time-Dependent Behavior: As time passes, the transient response will evolve.
   • If the circuit involves inductors or capacitors, the current can decay or rise exponentially to an eventual steady-state due to the charging/discharging rule or due to the inductive current response law (\( I = I_0 e^{-t/\tau} \), where \(\tau\) is the time constant).
   • The final state, as indicated in the answer, stabilizes to \( I = 1 \, \text{mA} \).
4. The other options are incorrect because:
   • I oscillates between 1 mA and 2 mA: This would imply the presence of an oscillator circuit like an LC tank, not mentioned here.
   • I = 1 mA at all t: Initial current at \( t=0 \) is \( 2 \, \text{mA} \).
   • I = 2 mA at all t: Steady current is \( 1 \, \text{mA} \); thus, it can't remain at \( 2 \, \text{mA} \).

Based on the above steps, it is reasonable to conclude that the given answer is correct: "at \( t = 0, I = 2 \, \text{mA} \) and with time it goes to \( 1 \, \text{mA} \)." This reflects an initial transient that settles into a steady-state value over time.