Final answer:
In an RC circuit with a 500 Ω resistor, 1.50 μF capacitor, and 6.16 V emf, the initial current is 0.01232 A, the RC time constant is 0.75 ms, the current after one-time constant is 0.00453 A, and the voltage on the capacitor after one time constant is 3.89 V.
Step-by-step explanation:
In an RC series circuit, the initial current (I_0) can be determined by Ohm's Law, where I_0 = emf / R.
Therefore, with an emf of 6.16 V and a resistance (R) of 500 Ω, the initial current is I_0 = 6.16 V / 500 Ω = 0.01232 A.
The RC time constant (T) is calculated by the product of the resistance (R) and the capacitance (C),
T = R × C.
For a 500 Ω resistor and a 1.50 μF capacitor, the time constant T = 500 Ω × 1.50 μF = 0.0005 ΩF = 0.75 ms.
After one time constant, the current in the circuit falls to 0.368 of the initial current due to the charging of the capacitor.
Thus, the current after one time constant is 0.01232 A × 0.368 = 0.00453 A.
The voltage on the capacitor after one-time constant can be calculated using the formula V = emf(1 - e-1) = emf × 0.632. Substituting the given emf, we get V = 6.16 V × 0.632 = 3.89 V.