What's the current in a 47-k.\Omega resistor with \(110 \mathrm{V}\) across it?

Ohm's Law is a fundamental principle in the field of electronics and electrical engineering. It defines the relationship between voltage, current, and resistance in an electrical circuit. The mathematical expression of Ohm's Law is given by the formula:
\[ I = \frac{V}{R} \]
where:

• \( I \) is the current in amperes (A),
• \( V \) is the voltage in volts (V),
• \( R \) is the resistance in ohms (\( \Omega \)).

Using Ohm's Law to calculate any one of these quantities requires the other two to be known. For example, if you wish to find the current (\( I \)) flowing through a component, you would need to know the voltage across the component and its resistance, as outlined in the exercise provided.
In more complex circuits with multiple resistors and power sources, Ohm's Law can be applied individually to each component or in combination with other circuit analysis techniques, such as Kirchhoff's circuit laws. Understanding how to calculate these relationships is essential for designing, analyzing, and troubleshooting electrical circuits.

In practical scenarios, resistance values may be presented in units other than ohms. For instance, it is common to encounter resistors labeled in kilo-ohms (\( k\Omega \)) or mega-ohms (\( M\Omega \)). Conversion between these units is crucial for accurate calculations.
To convert from kilo-ohms to ohms, as demonstrated in the step-by-step solution, you simply multiply the number of kilo-ohms by \(1000\):
\[ 1 k\Omega = 1000 \Omega \]
Similarly, to convert from mega-ohms to ohms, you would multiply by \(1,000,000\):
\[ 1 M\Omega = 1,000,000 \Omega \]
This conversion is an essential step before applying Ohm's Law since it ensures that all quantities are expressed in compatible units for the calculations. Always remember to check the units of each measurement and convert where necessary to avoid errors in your calculations.

Current is the rate at which charge flows through a conductor, and in a resistor, current depends on the voltage applied across it and the resistance it provides. The 'current in a resistor', therefore, refers to the amount of electric current that flows through the resistor due to the potential difference (voltage) across its terminals.
When you apply Ohm's Law, as seen in the problem's solution, you find that a higher resistance results in a lower current for a given voltage. This is reflective of the nature of a resistor, which is to oppose or resist the flow of current. It's important to note that the current calculated is the direct (DC) or steady-state current in the case of direct voltage being applied.
For alternating currents (AC), where voltages change over time, the concept still applies, but the effective or root-mean-square (RMS) values of voltage and current should be used. Calculating the current in a resistor is a fundamental skill in circuit analysis, and grasping this will help you understand how different components in a circuit influence the overall behavior of the electrical flow.