To find the combined resistance [tex]\( R_T \)[/tex] using the formula [tex]\(\dot{ R }_{ T } = \frac{R_1 \times R_2}{R_1 + R_2}\)[/tex], follow these steps:
1. Start with the given values:
- [tex]\( R_1 = 2.2 \, \text{k}\Omega \)[/tex]
- [tex]\( R_2 = 3.3 \, \text{k}\Omega \)[/tex]
2. Convert k[tex]\(\Omega\)[/tex] to [tex]\(\Omega\)[/tex]:
- [tex]\( R_1 = 2.2 \, \text{k}\Omega \)[/tex] is equivalent to [tex]\( 2.2 \times 10^3 \, \Omega = 2200 \, \Omega \)[/tex]
- [tex]\( R_2 = 3.3 \, \text{k}\Omega \)[/tex] is equivalent to [tex]\( 3.3 \times 10^3 \, \Omega = 3300 \, \Omega \)[/tex]
3. Substitute the values into the formula:
[tex]\[
R_T = \frac{R_1 \times R_2}{R_1 + R_2} = \frac{2200 \, \Omega \times 3300 \, \Omega}{2200 \, \Omega + 3300 \, \Omega}
\][/tex]
4. Calculate the numerator and the denominator:
- The numerator: [tex]\( 2200 \times 3300 = 7260000 \, \Omega^2 \)[/tex]
- The denominator: [tex]\( 2200 + 3300 = 5500 \, \Omega \)[/tex]
5. Divide the numerator by the denominator to find [tex]\( R_T \)[/tex]:
[tex]\[
R_T = \frac{7260000}{5500} = 1320 \, \Omega
\][/tex]
6. Convert the result back to k[tex]\(\Omega \)[/tex] for comparison:
[tex]\[
R_T = \frac{1320 \, \Omega}{1000} = 1.32 \, \text{k}\Omega
\][/tex]
7. Round the result to three decimal places:
[tex]\( R_T = 1.32 \, \text{k}\Omega \)[/tex]
Therefore, the combined resistance [tex]\( R_T \)[/tex] when [tex]\( R_1 = 2.2 \, k\Omega \)[/tex] and [tex]\( R_2 = 3.3 \, k\Omega \)[/tex] is:
[tex]\[
\boxed{1.32 \, k\Omega}
\][/tex]
