Final answer:
The time constant of the RC circuit with a 9.1 kΩ resistor and a 93 nF capacitor is calculated to be 846 μs, after conversion and rounding to the nearest integer.
Step-by-step explanation:
The time constant of an RC circuit is calculated using the formula T = R × C, where R is the resistance in ohms (Ω) and C is the capacitance in farads (F). The resistor has a value of 9.1 kΩ (kilohms), which is equivalent to 9100 Ω, and the capacitor has a value of 93 nF (nanofarads), which is equivalent to 93 × 10-9 F. To find the time constant in seconds, multiply the resistance by capacitance:
T = 9100 Ω × 93 × 10-9 F = 846300 × 10-9 seconds
As the question asks for the answer in microseconds (μs), convert seconds to microseconds by multiplying by 106:
T = 846300 × 10-9 × 106 μs = 846.3 μs
When rounded to the nearest integer, the time constant of the circuit is 846 μs.