What is the frequency of an ideal direct current (DC) signal in an electrical circuit?

Introduction / Context:
In electrical engineering and basic physics, we distinguish between direct current and alternating current. Alternating current varies periodically in magnitude and reverses direction, while direct current maintains a constant value and direction over time. Frequency is defined as the number of complete cycles of a repeating waveform per second and is measured in hertz. This question asks for the frequency of an ideal direct current signal, which is a simple conceptual test of your understanding of what frequency means in relation to time varying signals.

Given Data / Assumptions:
• Direct current is assumed to be perfectly steady over time, without fluctuations. • Frequency is defined only for signals that repeat in cycles. • We consider ideal DC, not ripple contaminated or switched DC. • Standard power system AC frequencies like 50 Hz and 60 Hz are included among the options.

Concept / Approach:
Frequency applies to periodic signals, such as sinusoidal alternating currents, square waves or any waveform that repeats a pattern over time. For alternating current in power systems, the waveform completes 50 or 60 cycles per second, leading to frequencies of 50 Hz or 60 Hz. An ideal direct current, by contrast, has a constant magnitude and does not vary with time. Because there is no oscillation, no cycles are completed in a given time interval. This means its frequency is zero hertz. You can think of DC as the zero frequency component of more general signals in Fourier analysis, reinforcing that its frequency is zero rather than any finite value.

Step-by-Step Solution:
Step 1: Recall that frequency is defined as number of cycles of a repeating waveform per second. Step 2: Understand that alternating currents and voltages have waveforms that change sign and shape periodically, so they have non zero frequencies. Step 3: Note that an ideal direct current is a constant value represented by a straight line when plotted against time. Step 4: Recognise that a constant signal does not complete any cycles because it never changes its value. Step 5: Conclude that the number of cycles per second is zero and therefore the frequency of ideal DC is zero hertz. Step 6: Select zero hertz from the options as the correct answer.

Verification / Alternative check:
From a mathematical point of view, any time varying signal can be decomposed into sinusoidal components with different frequencies. In such a representation, a constant or DC component corresponds to the term with frequency equal to zero. In phasor analysis and AC circuit theory, DC conditions are often described as the limiting case when frequency tends to zero. Practical DC supplies may have small ripple components due to imperfect rectification, but the idealised definition of direct current ignores these and treats DC as constant. Thus, both physical and mathematical viewpoints agree that DC has zero frequency.

Why Other Options Are Wrong:
Option B, 50 Hz, is the nominal mains frequency in many countries for AC power networks, not for DC. Option C, 60 Hz, is the mains frequency in some other countries, again associated with AC systems. Option D, 100 Hz, can occur as a ripple frequency in rectified AC circuits but is still an AC component, not pure DC. These non zero frequencies all describe alternating phenomena with repeated cycles; they cannot represent an ideal steady direct current.

Common Pitfalls:
Students sometimes confuse DC power supplies that are derived from AC mains, which may have ripple at twice the mains frequency, with perfectly steady DC. If they focus on the ripple frequency, they might mistakenly assign a non zero frequency to DC. Another pitfall is to think that because DC circuits can be switched on and off, they must have some frequency. Frequency, however, refers to periodic variation in a continuous signal, not occasional switching. Always remember that an ideal DC line on a time graph is flat, and a flat line has no cycles, so its frequency is zero hertz.

Final Answer:
The correct choice is Zero hertz, because an ideal direct current does not vary with time and therefore completes no cycles per second, giving it a frequency of zero.