A series circuit has two 5.0-ohm resistors and a power source of 9.0 volts. How will the current be affected and what will it be if another resistor (with a resistance of 7.5 ohms) is added to the circuit?

A.
increase; 0.51 amps
B.
increase; 0.72 amps
C.
increase; 3.6 amps
D.
decrease; 0.51 amps
E.
decrease; 0.72 amps

1 answer

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.