To analyze the effect of adding another resistor to the series circuit, we first need to calculate the total resistance and the current flowing through the circuit.
Step 1: Calculate the initial total resistance of the circuit with two 5.0-ohm resistors.
In a series circuit, the total resistance (R_total) is the sum of the individual resistances: \[ R_{\text{total initial}} = R_1 + R_2 = 5.0 , \text{ohms} + 5.0 , \text{ohms} = 10.0 , \text{ohms} \]
Step 2: Calculate the current using Ohm’s law (I = V/R).
Using the power source of 9.0 volts: \[ I_{\text{initial}} = \frac{V}{R_{\text{total initial}}} = \frac{9.0 , \text{V}}{10.0 , \text{ohms}} = 0.90 , \text{A} \]
Step 3: Add the third resistor (7.5 ohms) to the circuit and calculate the new total resistance.
\[ R_{\text{total new}} = R_1 + R_2 + R_3 = 5.0 , \text{ohms} + 5.0 , \text{ohms} + 7.5 , \text{ohms} = 17.5 , \text{ohms} \]
Step 4: Calculate the new current.
Using the same voltage (9.0 volts): \[ I_{\text{new}} = \frac{V}{R_{\text{total new}}} = \frac{9.0 , \text{V}}{17.5 , \text{ohms}} \approx 0.51 , \text{A} \]
Conclusion:
When an additional resistor with a resistance of 7.5 ohms is added to the circuit, the total resistance increases, leading to a decrease in current.
Thus, the answer is: D. decrease; 0.51 amps.