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 77.9 V is put across the plates of such a capacitor an electric field strength of [tex]$1.7 \frac{ kV }{ cm }[/tex] is measured.
Write an equation that will let you calculate the distance [tex]$d$[/tex] between the plates. Your equation should contain only symbols. Be sure you define each symbol.
Answer (1)
The electric field strength E is equal to the voltage V divided by the distance d : E = d V .
Solve for the distance d : d = E V .
Define the symbols: E is the electric field strength, and V is the voltage.
The equation to calculate the distance d is: d = E V
Explanation
Understanding the Problem The problem states 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. We are given the voltage V = 77.9 V and the electric field strength E = 1.7 c m kV . We need to find an equation for the distance d in terms of E and V .
Finding the Equation for Distance The relationship between electric field strength, voltage, and distance is given by the equation: E = d V We want to solve for d , so we multiply both sides by d and divide by E :
d = E V
Substituting the Values Now we can substitute the given values into the equation. We have V = 77.9 V and E = 1.7 c m kV . To keep the units consistent, we can convert E to c m V . Since 1 kV = 1000 V , we have E = 1.7 c m kV = 1.7 × 1000 c m V = 1700 c m V .
Now we can plug in the values: d = 1700 c m V 77.9 V = 0.0458 c m
Final Equation and Definitions The equation to calculate the distance d between the plates is: d = E V where: d is the distance between the plates, V is the voltage across the plates, and E is the electric field strength between the plates.
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. The equation d = E V is crucial in designing capacitors with specific voltage and electric field strength requirements. For instance, engineers use this equation to determine the appropriate distance between the capacitor plates to prevent electrical breakdown and ensure safe and efficient operation of the device. By understanding the relationship between voltage, electric field strength, and distance, engineers can optimize the performance and reliability of electronic circuits.
