## anonymous one year ago Three resistors connected in series have potential differences across them labeled V1, V2, and V3. What expresses the potential difference taken over the three resistors together?

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1. Michele_Laino

the current which flows into each of the three resistor, is such that: $\Large {R_1}I + {R_2}I + {R_3}I = {V_1} + {V_2} + {V_3}$ or: $\Large \left( {{R_1} + {R_2} + {R_3}} \right)I = {V_1} + {V_2} + {V_3}$

2. Michele_Laino

Now, the voltage drop: $\Large \left( {{R_1} + {R_2} + {R_3}} \right)I$ is equal to the voltage V applied to the battery to the three resitance, so we can write $\Large \left( {{R_1} + {R_2} + {R_3}} \right)I = V$

3. Michele_Laino

next, please substitute that last equation into the second one, and you will get your answer

4. anonymous

Thanks 😊