Question

A 15.0 Ω resistor is hooked up in series with a 12.0 Ω resistor followed by a 9.0 Ω resistor. The circuit is powered by a 12.0 V battery.
a.) Draw a labeled circuit diagram for the circuit described.
b.) Calculate the equivalent resistance.
c.) Calculate the voltage drop across each resistor in the circuit.

**How would this work? Thank you!! :)

Answer 1

please wait a moment

Answer 2

okie!:)

Answer 3

here is your circuit:

Answer 4

ohh okie :) whoahh so is that all that is needed for part a? :O

Answer 5

yes!

Answer 6

yay!! :) how do we do part b? :/

Answer 7

It is simple the equivalent resistance , is given by the sum of your resiatances, namely:
\[{R_{{\text{eq}}}} = {R_1} + {R_2} + {R_3} = ...?\]

Answer 8

ohh so 9+12+9=30? so part b equivalent resistance is 30 ohm?

Answer 9

I got 15+9+12=36

Answer 10

oh oops!! yes sorry, i do not know why i put 9 twice!! so yes, it would be 36 ohm is the eq. resistance?

Answer 11

yes!

Answer 12

yay!! okay, so last part? how do we do part c? :O

Answer 13

we have to compute the current of our circuit. that current intensity, is given by the subsequent formula:
\[I = \frac{V}{{{R_{{\text{eq}}}}}} = ...?\]

Answer 14

so 12/36? and we get 0.3333.... ? that is the voltage drop? :/

Answer 15

that's right! It is the current, no the voltage drop

Answer 16

ohh okay!! but part c asks for calculation of voltage drop across each resistor... how can we find that?

Answer 17

the requested voltage drops, can be computed using the Ohm's law, as below:
\[\begin{gathered}
{V_1} = {R_1}I = ...? \hfill \\
{V_2} = {R_2}I = ...? \hfill \\
{V_3} = {R_3}I = ...? \hfill \\
\end{gathered} \]

Answer 18

ohh so 15*0.33 = 4.95; 9*0.33=2.97 and 12 * 0.33=3.96

those are at the voltage drops?

Answer 19

that's right! Since I = 1/3, w better is:
\[\begin{gathered}
{V_1} = {R_1}I = \frac{{15}}{3} = 5volts \hfill \\
{V_2} = {R_2}I = \frac{{12}}{3} = 4volts \hfill \\
{V_3} = {R_3}I = \frac{9}{3} = 3volts \hfill \\
\end{gathered} \]

Answer 20

ohh okay!!! yay!! thank you!! is this problem finished? :O

Answer 21

oops.. Since I = 1/3, better* is:

Answer 22

yes! we have finished!

Answer 23

yay!! thank you so much!! :D

Answer 24

thank you!! :)