The electric field strength between the plates of a simple air capacitor is equal to the voltage across the plates divided by the distance between them. When a voltage of 61.1 V is put across the plates of such a capacitor an electric field strength of [tex]$3.3 \frac{ kV }{ cm }[/tex] is measured.
Write an equation that will let you calculate the distance [tex]$d$[/tex] between the plates. Your equation should contain only symbols. Be sure you define each symbol.
Answer (1)
Express the electric field strength as voltage divided by distance: E = d V .
Rearrange the equation to solve for the distance: d = E V .
Define the symbols: d is the distance, V is the voltage, and E is the electric field strength.
The equation for calculating the distance is: d = E V
Explanation
Understanding the Problem We are given that the electric field strength E between the plates of a capacitor is equal to the voltage V across the plates divided by the distance d between them. This relationship can be expressed as: E = d V We are given the voltage V = 61.1 V and the electric field strength E = 3.3 c m kV . Our goal is to find an equation for the distance d in terms of V and E .
Finding the Equation for d To find the distance d , we can rearrange the equation E = d V to solve for d . Multiplying both sides of the equation by d , we get: E d = V Now, dividing both sides by E , we obtain: d = E V
Defining the Symbols Now, let's define each symbol in the equation:
d represents the distance between the plates of the capacitor.
V represents the voltage across the plates.
E represents the electric field strength between the plates.
Calculating the Distance Therefore, the equation to calculate the distance d between the plates is: d = E V Given that E = 3.3 c m kV = 3300 c m V and V = 61.1 V , we can calculate the distance d :
d = 3300 c m V 61.1 V = 0.018515 c m So, the distance between the plates is approximately 0.0185 c m .
Examples
Capacitors are essential components in many electronic devices, such as smartphones, computers, and televisions. They store electrical energy and are used in various applications, including filtering, smoothing, and energy storage. Understanding the relationship between voltage, electric field strength, and distance in a capacitor is crucial for designing and analyzing electronic circuits. For example, if you need to build a capacitor with a specific capacitance and voltage rating, you would need to determine the appropriate distance between the plates based on the electric field strength of the dielectric material used.
