Resistors R1, R2, and R3 have resistances of 15.0 Ohms, 9.0 Ohms and 8.0 Ohms respectively. R1 and R2 are connected in series, and their combination is in parallel with R3 to form a load across a 6.0-V battery.
-What is the total resistance of the load?
-What is the current in R3
-What is the potential difference across R2?
First get the effective resistance of R1 and R2 in series. It is 24 ohms. That in parallel with 8 ohms has an overall circuit resistance Reff geiven by
1/Reff = 1/24 + 1/8 = 4/24 = 1/6
Therefore Reff = 6 ohms.
The total current going through the circuit (battery) is
I = V/Reff = 1.0 amperes.
The total current going through the R1 and R2 is V/(R1+R2) = 6/24 = 0.25 A
The potential drop across R2 is
0.25A*9 ohms = 2.25 V
a. Req = (R1+R2)R3/(R1+R2+R3) = (15+9)8/(15+9+8) = 6 Ohms.
I = E/Req = 6/6 = 1A.
b .I2+I3 = 1A.
I2 + 3I2 = 1,
I2 = 1/4 A.
I3 = 1-1/4 = 4/4-1/4 = 3/4 = 0.75A.
c. V2 = I2*R2 = 0.25 * 9 = 2.25 Volts.
Given:
R1 = 15 ohms
R2 = 20 ohms
R3 = 25 ohms
It = 12A
Solve for:
Rt = ?
Ed1 = R1
Ed2 = R2
Ed3 = R3
Et = ?
Ohm my goodness, let's dive into those circuits and have some fun with resistors!
To find the total resistance of the load, we need to first calculate the equivalent resistance of the series combination, R1 and R2. When resistors are in series, we simply add their resistances together. So, R1 + R2 = 15.0 Ohms + 9.0 Ohms = 24 Ohms.
Now, we have the equivalent resistance of the series combination, and we need to find the parallel combination with R3. When resistors are in parallel, we use the formula: 1/Req = 1/R1 + 1/R2 + ... + 1/Rn. In this case, R1 and R2 are in series, so we use their equivalent resistance as one of the terms: 1/Req = 1/24 Ohms + 1/8 Ohms. Let's simplify: 1/Req = (3 + 1)/24 Ohms = 4/24 Ohms = 1/6 Ohms. Flip both sides, and we get Req = 6 Ohms. Ta-da, the total resistance of the load is 6 Ohms!
Now, let's move on to the current in R3. To find the current, we can use Ohm's Law, which states that Current (I) is equal to Voltage (V) divided by Resistance (R). In this case, the voltage across the load is given as 6.0 V, and the resistance of R3 is 8.0 Ohms. So, I = 6.0 V / 8.0 Ohms = 0.75 A. The current flowing through R3 is 0.75 Amperes! It's electrifying!
Finally, let's calculate the potential difference across R2. Since R1 and R2 are connected in series, the potential difference across them is the same. We already know that the total voltage across the load is 6.0 V, and the voltage across R1 is also connected in series with R2, so the voltage across each resistor is proportionate to their resistance. Since R2 has a resistance of 9.0 Ohms and the total resistance of the series combination is 24 Ohms, we have V(R2) = (9.0 Ohms / 24 Ohms) * 6.0 V. Let's do some math: V(R2) = 0.375 * 6.0 V = 2.25 V. It's shocking, but the potential difference across R2 is 2.25 Volts!
I hope I've kept you amused while answering your questions about resistors and circuits. Remember, humor always helps provide a spark of excitement in learning!
To find the total resistance of the load, we need to first find the equivalent resistance of R1 and R2 in series, and then calculate the total resistance when R3 is added in parallel.
1. The total resistance of resistors R1 and R2 in series can be found by simply adding their resistances together:
R_total_series = R1 + R2
Therefore, R_total_series = 15.0 Ohms + 9.0 Ohms = 24.0 Ohms
2. The total resistance of the load when R1 and R2 are in series, and R3 is in parallel can be found using the formula for resistors in parallel:
1 / R_total_parallel = 1 / R_total_series + 1 / R3
Solving for R_total_parallel:
1 / R_total_parallel = 1 / 24.0 Ohms + 1 / 8.0 Ohms
Multiplying through by the common denominator of 24.0 Ohms * 8.0 Ohms:
1 / R_total_parallel = (8 / 192) + (24 / 192)
Simplifying:
1 / R_total_parallel = 32 / 192
Taking the reciprocal of both sides:
R_total_parallel = 192 / 32
Therefore, R_total_parallel = 6.0 Ohms
So, the total resistance of the load is 6.0 Ohms.
To find the current in R3, we can use Ohm's Law, which states that current (I) is equal to voltage (V) divided by resistance (R):
I = V / R
3. The current in R3 can be found by using the potential difference across the load (6.0 V) and the total resistance of the load (6.0 Ohms):
I = 6.0 V / 6.0 Ohms
Therefore, the current in R3 is 1.0 Ampere.
To find the potential difference across R2, we can again use Ohm's Law:
4. The potential difference across R2 can be found by using the current in R3 (1.0 Ampere) and the resistance of R2 (9.0 Ohms):
V_R2 = I * R2
Therefore, the potential difference across R2 is 1.0 Ampere * 9.0 Ohms = 9.0 Volts.
So, the potential difference across R2 is 9.0 Volts.