A signal has a measured period of 10 microseconds (10 µs). Using f = 1 / T, determine the frequency of this signal in hertz and select the closest option.

Introduction:
Period and frequency are reciprocals. Converting one to the other is a basic skill used across oscilloscopes, counters, and communication systems. Here we compute frequency from a given period in microseconds.

Given Data / Assumptions:

• Period T = 10 µs = 10 * 10^-6 s.
• Ideal periodic signal; measurement errors ignored.
• Use the reciprocal relation f = 1 / T.

Concept / Approach:
Compute f by taking the inverse of T and then convert to a convenient metric prefix. With microseconds, expect frequency in the tens or hundreds of kilohertz range.

Step-by-Step Solution:
1) Express T in seconds: T = 10 × 10^-6 s = 1 × 10^-5 s.2) Apply f = 1 / T: f = 1 / (1 × 10^-5) = 1 × 10^5 Hz.3) Convert to kHz: 1 × 10^5 Hz = 100 kHz.4) Select the closest option: 100 kHz.

Verification / Alternative check:
Sanity check: A 10 µs period implies 100,000 cycles per second; this aligns with typical PWM and microcontroller timing domains.

Why Other Options Are Wrong:
100 Hz and 1000 Hz: correspond to millisecond-level periods, not microseconds.
10 kHz: corresponds to T ≈ 100 µs, ten times larger than given.
1 MHz: corresponds to T = 1 µs, ten times smaller than given.

Common Pitfalls:
Forgetting to convert microseconds to seconds or mishandling powers of ten.

Final Answer:
100 kHz