# Max Voltage Across Capacitor & Resistor in a Circuit

• Engineering
• GalMichaeli
In summary, the circuit has a voltage source described by a pulse train with amplitude ±14 [Volts], and the capacitor initially acts as a short-circuit. To find the maximal voltage across the capacitor, one can use symmetry and write a KVL equation, which leads to a differential equation in capacitor voltage. Solving with the given initial condition yields the maximal voltage of the capacitor to be ±14 [Volts].
GalMichaeli

## Homework Statement

For the circuit in the picture below, with $V_{c}(t=0) = 0$ and a voltage source with period T described by
$$V_s(t) = \sum_{-\infty}^\infty (-1)^{n}g(t-nT)$$
where
$$g(t) = 7[u(t)-u(t-T)]\quad [Volt]$$
and $u(t)$ is a step function described by
$$u(t) = \begin{cases} 1 & \text{if } t \geq 0 \\ 0 & \text{if } t < 0 \end{cases}$$
What is the maximal voltages across the capacitor?
What is the maximal voltages across the resistor?

## The Attempt at a Solution

The voltage source is a pulse train with amplitude $\pm 14 \quad [Volts]$ and since at time $t = 0$ we may consider the cap. as a short-circuit, we have $V_{R}(t=0) = 14 \quad [Volts].$
I'm having trouble figuring out what the maximal voltage across the cap. is.
Should I apply transient analysis?

Thanx.

#### Attachments

• circuit.bmp
222.7 KB · Views: 492

First, never mind the voltage anywhere at t=0. You don't know what t=0 is. This voltage wavetrain has been running since t = -∞.

Now my gut reaction was Fourier series. But that's the hard way. Instead:

1. realize that v(t), the voltage across C, will vary symmetrically about zero volts since that is the average value of your input, from Vmin to Vmax = |Vmin|.

2.Then realize that the most negative C voltage is just before the input goes from -E to +E (why?). Then realize by symmetry that the max C voltage will occur just before the input transitions from +E to -E (again, be able to justify this statement).

3. Write the KVL: current thru R = current into C starting with t=0 at the -E to +E input transition. This will be a differential equation, easy to solve, in capacitor voltage v(t). Solve with the initial condition v(0+) = Vmin, then solve for v(T) = Vmax. The rest should "follow immediately" as the textbooks say.

## 1. What is the maximum voltage that can be applied across a capacitor and resistor in a circuit?

The maximum voltage that can be applied across a capacitor and resistor in a circuit depends on the specific values of the capacitor and resistor. In general, the maximum voltage is determined by the breakdown voltage of the capacitor and the power rating of the resistor. It is important to ensure that the applied voltage does not exceed these limits to prevent damage to the components.

## 2. How is the maximum voltage across a capacitor and resistor calculated?

The maximum voltage across a capacitor and resistor can be calculated using Ohm's Law. The formula is V = I x R, where V is the voltage, I is the current, and R is the resistance. In a circuit with a capacitor and resistor in series, the current is the same throughout the circuit. Therefore, the maximum voltage is equal to the current multiplied by the total resistance of the circuit.

## 3. What are the potential risks of exceeding the maximum voltage across a capacitor and resistor?

Exceeding the maximum voltage across a capacitor and resistor can lead to damage or failure of the components. This can result in a short circuit or fire, posing a safety hazard. It can also cause the circuit to malfunction or not operate as intended.

## 4. Are there any ways to increase the maximum voltage across a capacitor and resistor in a circuit?

There are a few ways to increase the maximum voltage across a capacitor and resistor in a circuit. One way is to use components with higher voltage ratings. Another way is to connect multiple capacitors and resistors in series, which increases the total voltage that can be applied across them. It is important to carefully consider the voltage ratings of all components in the circuit to prevent damage.

## 5. How does the frequency of the input signal affect the maximum voltage across a capacitor and resistor?

The frequency of the input signal does not directly affect the maximum voltage across a capacitor and resistor. However, higher frequencies may cause the capacitor to charge and discharge more frequently, which can increase the amount of heat generated in the resistor. This can potentially lead to overheating and damage. It is important to consider the frequency of the input signal when selecting components for a circuit.

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