To solve for the current in this combined circuit, we need to first find the equivalent resistance of both the parallel and series components, and then use Ohm's Law to find the total current.
Step 1: Find the equivalent resistance of the parallel resistors
The formula for two resistors in parallel \(R_1\) and \(R_2\) is given by:
\[ \frac{1}{R_{\text{parallel}}} = \frac{1}{R_1} + \frac{1}{R_2} \]
Plugging in the values:
\[ R_1 = 34.0 , \Omega \] \[ R_2 = 41.0 , \Omega \]
Calculating the equivalent resistance of the parallel resistors:
\[ \frac{1}{R_{\text{parallel}}} = \frac{1}{34.0} + \frac{1}{41.0} \]
Calculating each term:
\[ \frac{1}{34.0} \approx 0.02941 \] \[ \frac{1}{41.0} \approx 0.02439 \]
Now sum these values:
\[ \frac{1}{R_{\text{parallel}}} \approx 0.02941 + 0.02439 = 0.05380 \]
Now take the reciprocal to find \(R_{\text{parallel}}\):
\[ R_{\text{parallel}} \approx \frac{1}{0.05380} \approx 18.6 , \Omega \]
Step 2: Add the series resistor
The equivalent resistance \(R_{\text{total}}\) of the circuit is then the sum of the resistance of the parallel part and the series resistor:
\[ R_{\text{total}} = R_{\text{parallel}} + R_{\text{series}} = 18.6 , \Omega + 15.0 , \Omega = 33.6 , \Omega \]
Step 3: Use Ohm's Law to find the current
Using Ohm's Law, \(I = \frac{V}{R}\):
\[ V = 9.0 , \text{volts} \]
\[ I = \frac{9.0 , \text{volts}}{33.6 , \Omega} \]
Calculating the current:
\[ I \approx 0.2679 \text{ amps} \approx 0.27 \text{ amps} \]
Conclusion
The current in the circuit is approximately 0.27 amps. Therefore, the correct answer is C. 0.27 amps.
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