Two resistors of 15ohms and 5ohms are connected in parallel.this parallel combination is connected in a series with a third resistor of 10ohms.the whole circuit is then connected across a 40 volts supply. 1.determine the resistance of the circuit. 2.the current drawn from the supply.3.the volt drop across the 10ohm resistor. 4.the volt drop across the parallel branch.5.the current flow across the 15ohms. 6.the current flow across the 10ohms resistor.
1. R=(15*5)/(15+5) + 10=3.75 + 10=13.75 Ohms. = Resistance of the circuit.
2. I = E/R = 40/13.75 = 2.91 Amps.
3. V = I*R = 2.91 * 10 = 29.1 Volts.
4. V = I*R = 2.91 * 3.75 = 10.91 Volts.
5. I = V/R = 10.91/15 = 0.727 Amps.
6. I = V/R = 29.1/10 = 2.91 Amps.
To solve this circuit, we will follow these steps:
Step 1: Calculate the equivalent resistance of the parallel combination of the 15-ohm and 5-ohm resistors.
Step 2: Calculate the total resistance of the circuit by adding the 10-ohm resistor in series with the equivalent resistance from step 1.
Step 3: Calculate the current flowing through the circuit using Ohm's Law.
Step 4: Calculate the voltage drop across the 10-ohm resistor by multiplying the current from step 3 by the resistance.
Step 5: Calculate the voltage drop across the parallel branch using the fact that the voltage drop across parallel branches is the same.
Step 6: Calculate the current flowing through the 15-ohm resistor by dividing the voltage drop across the parallel branch from step 5 by the resistance.
Step 7: Calculate the current flowing through the 10-ohm resistor by subtracting the current through the 15-ohm resistor from the total current calculated in step 3.
Let's calculate each of these values:
1. Resistance of the circuit:
To find the equivalent resistance of the parallel combination, we use the formula:
1/Req = 1/R1 + 1/R2
1/Req = 1/15 + 1/5
1/Req = (1+3)/15
1/Req = 4/15
Req = 15/4 = 3.75 ohms
Now, adding the 10-ohm resistor in series, we find the total resistance:
Rt = Req + R3
Rt = 3.75 + 10
Rt = 13.75 ohms
Therefore, the resistance of the circuit is 13.75 ohms.
2. Current drawn from the supply:
Using Ohm's Law, we can calculate the current flowing through the circuit:
I = V/Rt
I = 40/13.75
I ≈ 2.909 Amps
So, the current drawn from the supply is approximately 2.909 Amps.
3. Voltage drop across the 10-ohm resistor:
Using Ohm's Law, we can calculate the voltage drop:
V = I * R
V = 2.909 * 10
V ≈ 29.09 Volts
So, the voltage drop across the 10-ohm resistor is approximately 29.09 Volts.
4. Voltage drop across the parallel branch:
The voltage drop across parallel branches is the same, and it is equal to the supply voltage, which is 40 Volts.
So, the voltage drop across the parallel branch is 40 Volts.
5. Current flow across the 15-ohm resistor:
Using Ohm's Law, we can calculate the current flowing through the 15-ohm resistor:
I = V/R
I = 40/15
I ≈ 2.667 Amps
So, the current flow across the 15-ohm resistor is approximately 2.667 Amps.
6. Current flow across the 10-ohm resistor:
We can calculate the current flowing through the 10-ohm resistor by subtracting the current flow across the 15-ohm resistor from the total current drawn from the supply:
I10 = Itotal - I15
I10 = 2.909 - 2.667
I10 ≈ 0.242 Amps
So, the current flow across the 10-ohm resistor is approximately 0.242 Amps.