Question

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?

Answer 1

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:
\[\Large \left( {{R_1} + {R_2} + {R_3}} \right)I = {V_1} + {V_2} + {V_3}\]

Answer 2

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
\[\Large \left( {{R_1} + {R_2} + {R_3}} \right)I = V\]

Answer 3

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

Answer 4

Thanks 😊