Answer:
The total resistance of these three resistors connected in parallel is ![1.7143\Omega](https://tex.z-dn.net/?f=1.7143%5COmega)
Step-by-step explanation:
The attached image has the circuit for finding the total resistance. The circuit is composed by a voltage source and three resistors connected in parallel:
,
and
.
<u>First step: to find the source current</u>
The current that the source provides is the sum of the current that each resistor consumes. Keep in mind that the voltage is the same for the three resistors (
,
and
).
![I_{R_1}=\frac{V_S}{R_1}](https://tex.z-dn.net/?f=I_%7BR_1%7D%3D%5Cfrac%7BV_S%7D%7BR_1%7D)
![I_{R_2}=\frac{V_S}{R_2}](https://tex.z-dn.net/?f=I_%7BR_2%7D%3D%5Cfrac%7BV_S%7D%7BR_2%7D)
![I_{R_3}=\frac{V_S}{R_3}](https://tex.z-dn.net/?f=I_%7BR_3%7D%3D%5Cfrac%7BV_S%7D%7BR_3%7D)
The total current is:
![I_S=I_{R_1}+I_{R_2}+I_{R_3}=\frac{V_S}{R_1}+\frac{V_S}{R_2}+\frac{V_S}{R_3}=\frac{R_2\cdot R_3 \cdot V_S+R_1\cdot R_3 \cdot V_S+R_1\cdot R_2 \cdot V_S}{R_1\cdot R_2\cdot R_3}](https://tex.z-dn.net/?f=I_S%3DI_%7BR_1%7D%2BI_%7BR_2%7D%2BI_%7BR_3%7D%3D%5Cfrac%7BV_S%7D%7BR_1%7D%2B%5Cfrac%7BV_S%7D%7BR_2%7D%2B%5Cfrac%7BV_S%7D%7BR_3%7D%3D%5Cfrac%7BR_2%5Ccdot%20R_3%20%5Ccdot%20V_S%2BR_1%5Ccdot%20R_3%20%5Ccdot%20V_S%2BR_1%5Ccdot%20R_2%20%5Ccdot%20V_S%7D%7BR_1%5Ccdot%20R_2%5Ccdot%20R_3%7D)
![I_S=V_S\cdot \frac{R_2\cdot R_3+R_1\cdot R_3+R_1\cdot R_2}{R_1\cdot R_2\cdot R_3}](https://tex.z-dn.net/?f=I_S%3DV_S%5Ccdot%20%5Cfrac%7BR_2%5Ccdot%20R_3%2BR_1%5Ccdot%20R_3%2BR_1%5Ccdot%20R_2%7D%7BR_1%5Ccdot%20R_2%5Ccdot%20R_3%7D)
The total resistance (
) is the source voltage divided by the source current:
![R_T=\frac{V_S}{I_S}](https://tex.z-dn.net/?f=R_T%3D%5Cfrac%7BV_S%7D%7BI_S%7D)
Now, replace
by the previous expression and the total resistance would be:
![R_T=\frac{V_S}{V_S\cdot \frac{R_2\cdot R_3+R_1\cdot R_3+R_1\cdot R_2}{R_1\cdot R_2\cdot R_3}}](https://tex.z-dn.net/?f=R_T%3D%5Cfrac%7BV_S%7D%7BV_S%5Ccdot%20%5Cfrac%7BR_2%5Ccdot%20R_3%2BR_1%5Ccdot%20R_3%2BR_1%5Ccdot%20R_2%7D%7BR_1%5Ccdot%20R_2%5Ccdot%20R_3%7D%7D)
Simplify the expression and you must get:
![R_T=\frac{R_1\cdot R_2\cdot R_3}{R_2\cdot R_3+R_1\cdot R_3+R_1\cdot R_2}](https://tex.z-dn.net/?f=R_T%3D%5Cfrac%7BR_1%5Ccdot%20R_2%5Ccdot%20R_3%7D%7BR_2%5Ccdot%20R_3%2BR_1%5Ccdot%20R_3%2BR_1%5Ccdot%20R_2%7D)
The last step is to replace the values of the resistors:
![R_T=\frac{(6\Omega )\cdot (3\Omega)\cdot (12\Omega)}{(3\Omega)\cdot (12\Omega)+(6\Omega)\cdot (12\Omega)+(6\Omega)\cdot (3\Omega)}=\frac{12}{7}\Omega=1.7143\Omega](https://tex.z-dn.net/?f=R_T%3D%5Cfrac%7B%286%5COmega%20%29%5Ccdot%20%283%5COmega%29%5Ccdot%20%2812%5COmega%29%7D%7B%283%5COmega%29%5Ccdot%20%2812%5COmega%29%2B%286%5COmega%29%5Ccdot%20%2812%5COmega%29%2B%286%5COmega%29%5Ccdot%20%283%5COmega%29%7D%3D%5Cfrac%7B12%7D%7B7%7D%5COmega%3D1.7143%5COmega%20)
Thus, the total resistance of these three resistors connected in parallel is ![1.7143\Omega](https://tex.z-dn.net/?f=1.7143%5COmega)
When exponent is negative, you just flip it to other side of <span>fraction.</span>
This is not enough information
Answer:
15000 - 750x
Step-by-step explanation:
Holly is trying to save $25, 000 to put a down payment on a condominium. She started with $10,000 and saved an additional $750 each month.
Let
y = dollars
x = number of months
Since she started her savings with $10, 000 her remaining amount to pay will be 25000 - 10000 = $15000 .
The amount will also be reducing by $750 per month
Therefore,
How far she is from her goal can be represented with the equation
15000 - 750x
Answer:
37.5
Step-by-step explanation:
0.1 pound for one batch of cookies
3.75 pound for x batches of cookies
3.75/0.1=x
he can make 37.5 batches of cookies