To solve the problem of finding the maximum capacitance that can be formed by combining three capacitors, we need to remember that capacitors in parallel sum up their capacitances. Here’s a step-by-step guide to finding the solution:
### Step 1: Convert the capacitances to Farads
Given capacitances are:
1. [tex]\(C_1 = 1600 \, \text{pF}\)[/tex]
2. [tex]\(C_2 = 5800 \, \text{pF}\)[/tex]
3. [tex]\(C_3 = 0.011 \, \mu\text{F}\)[/tex]
Convert these values to Farads:
- [tex]\(C_1 = 1600 \times 10^{-12} \, \text{F}\)[/tex]
- [tex]\(C_2 = 5800 \times 10^{-12} \, \text{F}\)[/tex]
- [tex]\(C_3 = 0.011 \times 10^{-6} \, \text{F}\)[/tex]
So, we get:
- [tex]\(C_1 = 1.6 \times 10^{-9} \, \text{F}\)[/tex]
- [tex]\(C_2 = 5.8 \times 10^{-9} \, \text{F}\)[/tex]
- [tex]\(C_3 = 1.1 \times 10^{-8} \, \text{F}\)[/tex]
### Step 2: Sum the capacitances in parallel
To find the total capacitance [tex]\(C_{\text{max}}\)[/tex] when the capacitors are connected in parallel, sum all the capacitances:
[tex]\[
C_{\text{max}} = C_1 + C_2 + C_3
\][/tex]
Plugging in the values:
[tex]\[
C_{\text{max}} = 1.6 \times 10^{-9} \, \text{F} + 5.8 \times 10^{-9} \, \text{F} + 1.1 \times 10^{-8} \, \text{F}
\][/tex]
### Step 3: Perform the addition
Add the capacitances:
[tex]\[
C_{\text{max}} = 1.6 \times 10^{-9} + 5.8 \times 10^{-9} + 11.0 \times 10^{-9}
\][/tex]
[tex]\[
C_{\text{max}} = 18.4 \times 10^{-9} \, \text{F}
\][/tex]
Converting this to scientific notation with two significant figures, we get:
[tex]\[
C_{\text{max}} = 1.84 \times 10^{-8} \, \text{F}
\][/tex]
The maximum capacitance that can be formed from the three given capacitors when connected in parallel is:
[tex]\[
C_{\text{max}} = 1.84 \times 10^{-8} \, \text{F}
\][/tex]
Thus, the correct answer, rounded to two significant figures, is:
[tex]\[
C_{\text{max}} = 1.8 \times 10^{-8} \, \text{F}
\][/tex]
Regards, please note that while the value 1.84 was initially correct to two decimal significant figures, the problem may have asked for an answer rounded to the nearest tenth in the scientific notation context. Adjust as per the specific requirements stated, here rounding could lead to:
[tex]\[
C_{\text{max}} = 1.8 \times 10^{-8} \text{F}
\][/tex]
