4.) Three 20-Ù resistors are connected in series to a 9-V battery. What is the voltage difference across each resistor?
5.) Three resistors of 5 Ù, 10 Ù, and 2 Ù are connected in parallel with one another. What is the equivalent resistance of this combination? Enter the unit as "ohms".
6.)Three identical resistnaces, each 24 Ù, are connected in parallel with one another and the combination is connected to a 12-V battery (See E12 Diagram on page 280 of your textbook). How much current flows through each resistor in this combination?
I've tried:
#4.) �¢V=IR convert to I=�¢V/Rseries
Rseries= R1 + R2+ R3 which is
2+2+2=6. then I took I=9V divided
by6. so I=1.5V....( get 3 tries on
online homework, it said 1.5 isn't
right, and im not sure what I had
done wrong.)
#5.) I did 1/Rparallel = 1/R1 +1/R2
+ R3. soo 1/Rp= 1/5+ 1/10 +1/2=
1/Rp=0.8...then I get 0.8ohms.
#6.) and for this one I did same as
number 5. but change the numbers
to: 1/Rparallel= 1/24+ 1/24 + 1/24.
1/Rparallel=0.125...I put it in
the I=�¢V/R equation, so I=12v/0.125 and I get 96A
To answer these questions, we need to understand the concepts of series and parallel circuits, Ohm's law, and how to calculate equivalent resistance.
4.) In order to find the voltage difference across each resistor in a series circuit, we need to know the total resistance and the battery voltage. In this case, the three 20-Ù resistors are connected in series to a 9-V battery. Since they are connected in series, the total resistance (RT) is the sum of the individual resistances (R1, R2, R3).
RT = R1 + R2 + R3 = 20 Ù + 20 Ù + 20 Ù = 60 Ù
Now, to find the voltage difference across each resistor (V1, V2, V3), we can use Ohm's law:
V = IR
Since the resistors are connected in series, the current (I) passing through each resistor will be the same. Let's call it I_total.
I_total = V / RT = 9 V / 60 Ù = 0.15 A
Therefore, the voltage difference across each resistor will be:
V1 = V2 = V3 = I_total * R = 0.15 A * 20 Ù = 3 V
So, the voltage difference across each resistor is 3 V.
5.) To calculate the equivalent resistance in a parallel circuit, we can use the formula:
1/RTotal = 1/R1 + 1/R2 + 1/R3
Plugging in the values:
1/RTotal = 1/5 Ù + 1/10 Ù + 1/2 Ù
To simplify the equation, we can find a common denominator and combine the fractions:
1/RTotal = 2/10 Ù + 1/10 Ù + 5/10 Ù
1/RTotal = 8/10 Ù
To get the reciprocal of both sides, we have:
RTotal = 10 Ù / 8 = 1.25 Ù
So, the equivalent resistance of this combination is 1.25 ohms.
6.) In a parallel circuit, the voltage across each resistor is the same, which is equal to the voltage of the battery. In this case, the voltage across each resistor is 12 V. To find the current (I) flowing through each resistor, we can use Ohm's law:
I = V / R
For each resistor, the current (I) will be:
I = 12 V / 24 Ù = 0.5 A
So, the current flowing through each resistor in this combination is 0.5 A.