Final answer:
The initial current in the series circuit is 0.012 A, which corresponds to option (a). The RC time constant is 7.5e-4 s. After one time constant, the current is 0.004416 A and the voltage on the capacitor is 3.89 V.
Step-by-step explanation:
Calculating the Initial Current in a Series Circuit
To find the initial current (I) in a series circuit with an uncharged capacitor, a resistor, and a voltage source, you use Ohm's Law: I = V / R, where V is the voltage and R is the resistance. In this case, the initial voltage across the resistor is the same as the emf of the voltage source before the capacitor begins to charge. Since the capacitor is initially uncharged, it has no voltage across it and does not affect the initial current.
Initial Current Calculation:
The initial current is I = 6.16 V / 500 Ω = 0.01232 A.
This can be rounded to 0.012 A, which corresponds to option (a).
Calculating the RC time constant (tau, τ):
τ = R × C = 500 Ω × 1.50 µF = 0.0005 ΩF × 1.50 µF = 0.00075 s or 7.5 × 10-4 s.
Current after one time constant:
After one time constant, the current decreases to 36.8% of its initial value. Thus, I = 0.012 A × 0.368 = 0.004416 A.
Voltage on the capacitor after one time constant:
The voltage on the capacitor after one time constant is 63.2% of the final voltage (emf), which is 6.16 V × 0.632 = 3.89 V.