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 d to get the equation for the distance between the plates: d = E V .
Define the symbols: d is the distance, V is the voltage, and E is the electric field strength.
The final equation is d = E V , where E = 1.7 c m kV and V = 77.9 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 .
Relating Electric Field, Voltage, and Distance The relationship between electric field strength, voltage, and distance is given by the equation: E = d V To find the distance d , we need to rearrange this equation to solve for d .
Solving for Distance Multiplying both sides of the equation by d , we get: E "." d = V Now, divide both sides by E to isolate d :
d = E V This is the equation we will use to calculate the distance d .
Defining the Symbols Now we define the symbols used in the equation: d = distance between the plates V = voltage across the plates E = electric field strength between the plates
Final Equation and Definitions The equation to calculate the distance d between the plates is: d = E V where: E = 1.7 c m kV is the electric field strength V = 77.9 V is the voltage across the plates
Examples
Capacitors are essential components in many electronic devices, such as smartphones, computers, and audio equipment. They store electrical energy and are used in circuits for filtering, smoothing, and timing. The equation d = E V is crucial in designing capacitors with specific properties. For instance, if an engineer needs a capacitor with a certain voltage rating and electric field strength, they can use this equation to determine the necessary distance between the plates. This ensures the capacitor operates safely and efficiently within the device.
