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 battery is disconnected,its terminal voltage is 9.4 V.What is the internal resistance of the battery?

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 battery is disconnected,its terminal voltage is 9.4 V.What is the internal resistance of the battery?

Quizplus · Accepted Answer

First, we need to determine the total resistance of the circuit.
Recall that the total resistance of a series circuit is the sum of the individual resistances:
R_total = R1 + R2 + R3

Using the given values:
R_total = (11eaa64f_8ff2_4e08_a696_073e3274490f_TB5258_11) + (11eaa64f_8ff2_4e09_a696_a736ed6f092e_TB5258_11) + (11eaa64f_8ff2_751a_a696_abb1e99df363_TB5258_11)
R_total = 11eaa64f_8ff2_c335_a696_9c7e2d2f4915_TB5258_11

Next, we can use Ohm's Law to find the current in the circuit:
V = IR
I = V/R_total

Using the given terminal voltage when connected to the battery:
I = (11eaa64f_8ff2_751b_a696_4b99de38ecd8_TB5258_11) / (11eaa64f_8ff2_c335_a696_9c7e2d2f4915_TB5258_11)
I = 11eaa64f_8ff2_c33e_a696_a1a75847543e_TB5258_11

When the battery is disconnected, the current through the circuit would be zero. This means that the voltage across the internal resistance of the battery would be equal to the terminal voltage when disconnected:
V_internal = 11eaa64f_8ff2_c33c_a696_4e3e090ecf4a_TB5258_11

Using Ohm's Law again:
V_internal = IR_internal
R_internal = V_internal / I

R_internal = (11eaa64f_8ff2_c33c_a696_4e3e090ecf4a_TB5258_11) / (11eaa64f_8ff2_c33e_a696_a1a75847543e_TB5258_11)
R_internal = 0.8 11eaa64f_8ff2_c33d_a696_b1e166976304_TB5258_11

Therefore, the best choice is B.

Resistors Having Values of , ,And Are