A 16.0 ohm and a 24.0 ohm resistor are connected in parallel. A difference in potential of 32.0 V is applied to the combination.
What is the equivalent resistance of the parallel circuit?
What is the total current in the circuit?
Compute the equivalent resistance R with the equation
1/R = 1/R1 + 1/R2,
which can be rearranged to give
R = R1 R2/(R1 + R2)
I = V/R (use the equivalent R)
To find the equivalent resistance of the parallel circuit, you can use the formula:
1/Req = 1/R1 + 1/R2
Where:
Req = equivalent resistance of the parallel circuit
R1 = resistance of the first resistor
R2 = resistance of the second resistor
In this case, R1 = 16.0 ohm and R2 = 24.0 ohm.
1/Req = 1/16.0 + 1/24.0
Now, we can solve for Req:
1/Req = (3/48 + 2/48) / 48
1/Req = 5/48 / 48
1/Req = 5 / (48 * 48)
1/Req = 5 / 2304
Req = 2304 / 5
Therefore, the equivalent resistance of the parallel circuit is approximately 460.8 ohms.
To find the total current in the circuit, you can use Ohm's Law:
I = V / R
Where:
I = total current in the circuit
V = applied potential difference (given as 32.0 V)
R = equivalent resistance of the parallel circuit (found to be 460.8 ohms)
I = 32.0 / 460.8
Therefore, the total current in the circuit is approximately 0.0694 A (or 69.4 mA).
To find the equivalent resistance of a parallel circuit, you can use the formula:
1/Req = 1/R1 + 1/R2 + ...
Where Req is the equivalent resistance, R1, R2, etc. are the resistances of the individual components connected in parallel.
In this case, the resistances of the two resistors are given as 16.0 ohms and 24.0 ohms, respectively. Plugging these values into the formula, we get:
1/Req = 1/16.0 + 1/24.0
To simplify this equation, you can find a common denominator for the fractions:
1/Req = (3/48) + (2/48)
Adding these fractions:
1/Req = 5/48
To isolate Req, you can take the reciprocal of both sides:
Req = 48/5
Therefore, the equivalent resistance of the parallel circuit is 48/5 ohms or 9.6 ohms.
To find the total current in the circuit, you can use Ohm's Law, which states that the current (I) flowing through a circuit is equal to the voltage (V) divided by the resistance (R):
I = V/R
In this case, the voltage applied to the combination is given as 32.0 V, and the equivalent resistance is 9.6 ohms. Plugging these values into the formula, we get:
I = 32.0/9.6
Simplifying this equation:
I = 3.33 A
Therefore, the total current in the circuit is approximately 3.33 Amperes.