A 6.0 Ù resistor and a 3.0 Ù resistor are connected in parallel to a 1.5 V battery of negligible internal resistance. What is the current in the 3.0 Ù
resistor?
Well, if you have a 6.0 Ù resistor and a 3.0 Ù resistor connected in parallel, they must be having a serious conversation. Maybe the 6.0 Ù resistor is telling the 3.0 Ù resistor a shocking joke! 😄 But let's get back to the question at hand.
In a parallel circuit, the voltage across each resistor is the same, but the current divides amongst them. So, to find the current in the 3.0 Ù resistor, we need to calculate it using Ohm's Law.
Since the battery has a voltage of 1.5V and the resistors are in parallel, the voltage across the 3.0 Ù resistor is also 1.5V. Using Ohm's Law (V = I * R), we can rearrange the formula to solve for current (I = V / R). Plugging in the values, we get:
I = 1.5V / 3.0 Ù = 0.5 A
So, the current in the 3.0 Ù resistor is 0.5 Amps. Remember, resistors may be serious, but you can always find a little humor in the science! 😄
To find the current in the 3.0 Ω resistor, we first need to determine the equivalent resistance of the parallel combination of the 6.0 Ω and 3.0 Ω resistors.
The formula to find the equivalent resistance of two resistors in parallel is:
1/Req = 1/R1 + 1/R2
Where Req is the equivalent resistance, R1 is the resistance of the first resistor, and R2 is the resistance of the second resistor.
In this case, R1 = 6.0 Ω and R2 = 3.0 Ω. Substituting these values into the formula, we get:
1/Req = 1/6.0 + 1/3.0
Simplifying this equation gives us:
1/Req = (1 + 2)/6.0
1/Req = 3/6.0
1/Req = 1/2
Therefore, the equivalent resistance of the parallel combination is 2.0 Ω.
Next, we can use Ohm's law to find the current flowing through the circuit. Ohm's law states that the current (I) is equal to the voltage (V) divided by the resistance (R):
I = V/R
In this case, V = 1.5 V and R = 2.0 Ω. Substituting these values into the formula, we get:
I = 1.5 / 2.0
Simplifying this equation gives us:
I = 0.75 A
Therefore, the current in the 3.0 Ω resistor is 0.75 A.
To find the current in the 3.0 Ω resistor, we first need to calculate the total resistance of the parallel combination of the two resistors.
In a parallel circuit, the total resistance (R_tot) is given by the formula:
1/R_tot = 1/R1 + 1/R2 + ...
Where R1, R2, ... are the resistances of individual resistors in the circuit.
In this case, we have two resistors connected in parallel, so we can substitute the values into the formula as follows:
1/R_tot = 1/6.0 Ω + 1/3.0 Ω
Simplifying this equation:
1/R_tot = (1/6.0) + (2/6.0) = 3/6.0 = 0.5
Taking the reciprocal of both sides of the equation:
R_tot = 1/0.5 = 2.0 Ω
So, the total resistance of the parallel combination is 2.0 Ω.
Next, we can use Ohm's Law (V = I * R) to find the current (I) flowing through the 3.0 Ω resistor. We know the voltage (V) across the circuit, which is 1.5 V, and the resistance (R), which is 3.0 Ω.
Rearranging the formula:
I = V / R = 1.5 V / 3.0 Ω = 0.5 A
Therefore, the current flowing through the 3.0 Ω resistor is 0.5 Amps.
I = V/R = 1.5/3 = 0.5A.
The voltage across each resistor is 1.5
volts.