A student in the laboratory connects a 13 Ω resistor, a 24 Ω resistor, and a 41 Ω resistor in parallel and then connects the arrangement to a 43 V dc source. What is the current? What is the power? (in watts)
E = 43 Volts.
R1 = 13 Ohms
R2 = 24 Ohms
R3 = 41 Ohms
I = I1 + I2 + I3 =
E/R1 + E/R2 + E/R3 =
43/13 + 43/24 + 43/41 =
3.31 + 1.79 + 1.05 = 6.15 Amps. = Total
current drawn from the 43-volt source.
P = E*I = 43 * 6.15 = 264.5 Watts = Total power taken from the 43-volt source.
P1 = E^2/R1
P2 = E^2/R2
P3 = E^2/R3
P = P1 + P2 + P3.
To find the current in the parallel circuit, we can use Ohm's Law which states that current (I) is equal to the voltage (V) divided by the total resistance (R):
I = V / R
In this case, the total resistance (R) is given by the formula:
1/R_total = 1/R1 + 1/R2 + 1/R3
where R1, R2, and R3 are the individual resistances.
Let's calculate the total resistance first:
1/R_total = 1/13 + 1/24 + 1/41
Now, we'll calculate the inverse of the total resistance:
R_total = 1 / (1/13 + 1/24 + 1/41)
= 1 / (0.076923 + 0.041667 + 0.02439)
= 1 / 0.14398
≈ 6.938 Ω
Now, we can find the current:
I = V / R_total
= 43 / 6.938
≈ 6.192 A
Therefore, the current flowing through the circuit is approximately 6.192 A.
To calculate the power, we use the formula:
P = IV
P = 6.192 * 43
≈ 266.056 W
Therefore, the power dissipated in the circuit is approximately 266.056 watts.
To find the current in a parallel circuit, you can use Ohm's Law. Ohm's Law states that the current (I) flowing through a circuit is equal to the voltage (V) divided by the resistance (R):
I = V / R
First, let's find the equivalent resistance for the three resistors in parallel. In a parallel circuit, the reciprocal of the equivalent resistance (1/Req) is equal to the sum of the reciprocals of the individual resistances (1/R1 + 1/R2 + 1/R3):
1/Req = 1/R1 + 1/R2 + 1/R3
1/Req = 1/13 + 1/24 + 1/41
Calculating this expression gives us the value of 0.117Ω for Req.
Next, we can use Ohm's Law to find the current flowing through the circuit. Since we have the voltage (43V) and the resistance (0.117Ω), we can substitute these values into the equation:
I = 43V / 0.117Ω
Calculating this expression gives us the value of approximately 367.52A for the current flowing through the circuit.
To calculate the power (P) in watts, we can use the formula:
P = V * I
Substituting the values gives us:
P = 43V * 367.52A
Calculating this expression gives us a power value of approximately 15,805.36 watts for the circuit.
Therefore, the current flowing through the circuit is approximately 367.52A, and the power consumed by the circuit is approximately 15,805.36 watts.