A capacitor is connected in the circuit shown with two resistors, R A and R B .
ID: 1420305 • Letter: A
Question
A capacitor is connected in the circuit shown with two resistors, RA and RB. Resistor RA has a resistance of 2R, while resistor RB has a resistance of R. The emf of the battery, which has negligible internal resistance, is 9.00 V. At the instant the switch is closed, the capacitor also happens to have a potential difference of 9.00 V, with the top plate having a higher potential.
Which of the following statements apply to this circuit after the switch is closed? (Select all that apply. You need to select all the true statements to get credit for this question.)
1. The two resistors are in series, so the current through resistor A is always equal to the current through resistor B.
2. The current through the two resistors is the same initially, but as more time passes the greater the difference there is between their currents.
3. The current through the two resistors is different initially, but as more time passes the smaller the difference there is between their currents.
4. The current through resistor B is always twice as large as that through resistor A.
5. The current through resistor A is constant but that through resistor B changes with time.
6. The current through resistor A changes with time but that through resistor B is constant.
7. As time passes, the capacitor voltage approaches zero.
8. As time passes, the capacitor voltage approaches 3.00 V.
9. As time passes, the capacitor voltage approaches 6.00 V.
10. As time passes, the capacitor voltage stays constant at 9.00 V.
The answer is not 4; (3, 5, 7); (3, 7); or 3.
Explanation / Answer
Initially, when capacitor plates are at same potential as the battery itself, there is no current flowing through resistor A. When the switch is closed, Capacitor starts discharging through resistor B. Thus there is a large current flowing through resistor B. As the potential difference across the plates of the capacitor starts decreasing in the process, current starts flowing through resistor A also.
The current through the two resistors is different initially, but as more time passes the smaller the difference there is between their currents.
When steady state is reached, no more charging and discharging of the capacitor occurs. As the capacitor is in parallel with the resistor B, therefore the potential difference across the plates of the capacitor becomes equal to that across resistor B i.e. 3.00 V.
Hence statements 3 and 8 are correct.
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