Extra Credit 3/26/19
$$R_2$$
$$R_1$$
$$\Delta V$$
$$R_3$$
Consider the circuit shown: Three resistors are connected to a battery with negligible internal resistance. $$R_1$$ and $$R_2$$ are identical ($$R_1 = R_2 = R$$) and $$R_3$$ has twice the resistance of $$R_1$$ and $$R_2$$ ($$R_3 = 2R$$).
a. Let $$I_1$$, $$I_2$$, and $$I_3$$ be the currents through resistors $$R_1$$, $$R_2$$, and $$R_3$$, respectively. Rank the currents from greatest to least. Justify your ranking by reasoning from physical principles.
b. Let $$\Delta V_1$$, $$\Delta V_2$$, and $$\Delta V_3$$ be the potential differences across resistors $$R_1$$, $$R_2$$, and $$R_3$$, respectively. Rank the potential differences from greatest to least. Justify your ranking by reasoning from physics principles.
c. Through which of the resistors shown is electric energy being converted to other forms at the greatest rate? Explain your choice.
d. A student is given an ammeter and a voltmeter and asked to determine the numerical value of the resistance R. Draw a diagram indicating how the student could insert the meters in the circuit shown so that they would yield values that could be used to calculate the resistance R. Indicate how the student would use these values to calculate the resistance R.
e. On the circuit diagram, add another wire that will cause the current through resistor $$R_3$$ to decrease, while allowing the current through resistor $$R_1$$ to remain unchanged. Explain your reasoning.
