(1) Imagine a single-loop circuit with a battery, and three resistors R1, R2, R3 connected in series. Resistance is ignorable except for the resistors. Resistors are ohmic. Answer the following questions 2. a. (0.5) Which (if any) physical quantity- among resistance R, current I, and voltage V must be the same for the three resistors? b. (0.5) How are R, I, and V related for each resistor in this circuit? Answer with an equation involving these three quantities.

## Answer

Let consider a circuit such that 3 resistances R_1, R_2 & R_3 are connected in series to a battery of v volt cause a current I to flow. Since these resistances are connected in series so the same current will flow through the resistances. Hence current I is same for all 3 resistances. Let R be the equivalent resistance of circuit, hence R = R_1 + R_2 + R_3, by ohm’s law I = V/R or V/R_1 + R_2 + R_3 let V_1 = I R_1 = V R_1/R_1 + R_2 + R_3, V_2 = I R_2 = V R_2/R_1 + R_2 + R_3, V_3 = I R_3/R_1 + R_2 + R_3 where V_1, V_2 & V_3 are the voltage drop across resistors R_1, R_2 & R_3