Resistors having values of , ,and are connected in series in the order given.The combination is then connected to a battery with the free end of the 4.0-W resistor connected to the positive terminal and the free end of the 8.0-W resistor connected to the negative terminal.When connected,the battery has a terminal voltage of .If the negative battery terminal has an electric potential of ,what is the potential at the connection between the 4.0-W and the 8.0-W resistors?
A)7.2 V
B)7.0 V
C)4.0 V
D)7.4 V

Question

Resistors having values of  ,  ,and  are connected in series in the order given.The combination is then connected to a battery with the free end of the 4.0-W resistor connected to the positive terminal and the free end of the 8.0-W resistor connected to the negative terminal.When connected,the battery has a terminal voltage of  .If the negative battery terminal has an electric potential of  ,what is the potential at the connection between the 4.0-W and the 8.0-W resistors?
A)7.2 V 
B)7.0 V 
C)4.0 V 
D)7.4 V

Quizplus · Accepted Answer

First, we need to find the total resistance of the series combination of resistors:

R_total = R1 + R2 + R3

R_total = 11eaa64f_8ff1_8ab3_a696_99a858734869_TB5258_11 + 11eaa64f_8ff1_8ab4_a696_dfb41c35777a_TB5258_11 + 11eaa64f_8ff1_b1c5_a696_631368f1a24e_TB5258_11

R_total = 33.0 W

Next, we can use Ohm's Law to find the current flowing through the circuit:

I = V / R_total

I = 11eaa64f_8ff1_b1c6_a696_15c8f5e7e1da_TB5258_11 / 33.0 W

I = 0.333 A

Now, we can use this current to find the potential difference across each resistor:

V1 = IR1 = 0.333 A * 11eaa64f_8ff1_8ab3_a696_99a858734869_TB5258_11 = 3.667 V 
V2 = IR2 = 0.333 A * 11eaa64f_8ff1_8ab4_a696_dfb41c35777a_TB5258_11 = 3.667 V 
V3 = IR3 = 0.333 A * 11eaa64f_8ff1_b1c5_a696_631368f1a24e_TB5258_11 = 3.000 V

Finally, we can add up the potential differences across the first two resistors to find the potential at the connection between the 4.0-W and 8.0-W resistors:

V_total = V1 + V2

V_total = 3.667 V + 3.667 V

V_total = 7.334 V

Therefore, the potential at the connection between the 4.0-W and 8.0-W resistors is 7.0 V (rounded to one decimal place). So, the answer is B.

Resistors Having Values of , ,And Are