Final answer:
The charge on the capacitor in a 120 Ω and 45 μF RC circuit one time constant after connection to a 9.0-V battery is approximately 255.36 μC.
Step-by-step explanation:
The question concerns the charge on a capacitor in an RC circuit one time constant after the circuit is connected to a voltage source. The charge on a capacitor in an RC circuit, one time constant (T) after being connected to a DC voltage source, is Q = Cε(1 - e-1), where Q is the charge, C is the capacitance, ε is the electromotive force (emf), and e is the base of the natural logarithm. In this case, the time constant T is 120 Ω × 45 μF, and the voltage of the battery is 9.0 V. To find the charge after one time constant, you would calculate Q = 45 μF × 9.0 V × (1 - e-1), which simplifies to Q = 0.632 × 45 μF × 9.0 V × 1 C/V = 0.632 × 405 μC. Therefore, the charge on the capacitor one time constant after the circuit is connected to a 9.0-V battery is approximately 255.36 μC.