*Question E5B04:
What is the time constant of a circuit having two 220-microfarad capacitors and two 1-megohm resistors, all in parallel?*  

*Correct Answer is  D: 220 seconds*  

### AI Response: (may contain errors)  

To find the time constant of a circuit with capacitors and resistors in parallel, we use the formula for the time constant $\tau$:

$$\tau = R_{eq} \times C_{eq}$$

where:
- $R_{eq}$ is the equivalent resistance,
- $C_{eq}$ is the equivalent capacitance.

### Step 1: Calculate Equivalent Capacitance ($C_{eq}$)

For capacitors in parallel, the equivalent capacitance is the sum of the individual capacitances:

$$C_{eq} = C_1 + C_2$$

In this case, we have two 220-microfarad capacitors:

$$C_{eq} = 220 \, \mu F + 220 \, \mu F = 440 \, \mu F$$

### Step 2: Calculate Equivalent Resistance ($R_{eq}$)

For resistors in parallel, the equivalent resistance is given by:

$$\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2}$$

For two 1-megohm resistors:

$$\frac{1}{R_{eq}} = \frac{1}{1 \, M\Omega} + \frac{1}{1 \, M\Omega} = \frac{2}{1 \, M\Omega}$$

Thus, 

$$R_{eq} = \frac{1 \, M\Omega}{2} = 0.5 \, M\Omega = 500,000 \, \Omega$$

### Step 3: Calculate the Time Constant ($\tau$)

Now we can calculate the time constant:

$$\tau = R_{eq} \times C_{eq}$$

Substituting the values we found:

$$\tau = 500,000 \, \Omega \times 440 \times 10^{-6} \, F$$

Calculating this gives:

$$\tau = 500,000 \times 0.000440 = 220 \, seconds$$

### Conclusion

- **Correct Answer: 220 seconds**  
  This is the time constant for the given circuit configuration.

### Why Other Choices Are Incorrect

- **A: 55 seconds**  
  This value does not correspond to the calculated time constant and likely results from incorrect calculations or assumptions about the circuit.

- **B: 110 seconds**  
  This value could arise from miscalculating the equivalent resistance or capacitance but does not match the correct calculations.

- **C: 440 seconds**  
  This value might be mistakenly derived from only considering the capacitance without accounting for the resistance in the circuit.

### Summary of Key Formulas

- Time constant: 
  $$\tau = R_{eq} \times C_{eq}$$
- Equivalent capacitance (parallel):
  $$C_{eq} = C_1 + C_2$$
- Equivalent resistance (parallel):
  $$\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2}$$

Understanding these concepts will help you solve similar problems on the Extra Class exam.