In the circuit at right, two resistors are connected in parallel.
What is the voltage across the 4 Ω resistor?
What is the voltage across the 12 Ω resistor?
if the resistors are in parallel , the voltage should be the same
To determine the voltage across each resistor in a parallel circuit, you need to know the current flowing through the circuit and the total resistance.
First, let's calculate the current flowing through the circuit. Assuming a voltage source is connected to the circuit, we need to know the value of the voltage (V) and the total resistance (Rtotal) of the circuit.
Next, we can calculate the total resistance (Rtotal) of the circuit by using the formula:
1/Rtotal = 1/R1 + 1/R2 + ...
In this case, as there are only two resistors connected in parallel, we can calculate the total resistance (Rtotal) using the formula:
1/Rtotal = 1/R1 + 1/R2
Once we have the total resistance, we can calculate the current (I) flowing through the circuit using Ohm's Law:
I = V / Rtotal
Now, we can find the voltage across each resistor by multiplying the current (I) by the resistance (R) using Ohm's Law:
Voltage across a resistor (V) = I * R
Using these steps, let's determine the voltage across each resistor:
1. Voltage across the 4 Ω resistor:
- Calculate the total resistance (Rtotal) using the formula:
1/Rtotal = 1/4 + 1/12
- Solve for Rtotal to get the reciprocal value and then take the reciprocal again:
Rtotal = 1/(1/4 + 1/12)
- Calculate the current flowing through the circuit:
I = V / Rtotal
- Substitute the given values and calculate the current:
I = V / (1/(1/4 + 1/12))
- Substitute the value of the current into Ohm's Law to find the voltage across the 4 Ω resistor:
Voltage across the 4 Ω resistor (V4) = I * 4
2. Voltage across the 12 Ω resistor:
- Calculate the voltage across the 12 Ω resistor using the same formula:
Voltage across the 12 Ω resistor (V12) = I * 12
By following these steps and using the given values, you can calculate the voltage across the 4 Ω resistor and the voltage across the 12 Ω resistor in the given circuit.