A battery has an emf of 8V and an internal resistance 2ohms. If it is connected to an external circuit that draws 6W of power, what is a possible current in the circuit?
Please give me some ideas to do it! THANKS!
call the unknown current i
6 = i^2 R outside
so R = 6/i^2
total resistance = 2 + (6/i^2)
E = i *total resistance
8 = i (2 + (6/i^2) )
8 = 2 i + 6/i
2 i^2 -8i + 6 = 0
i^2 - 4 i + 3 = 0
(i-3)(i-1) = 0
i = 3 or i = 1
which of those solutions makes sense
if i = 3 then
V loss internal = 2 * 3 = 6 volts
only 2 volts external, most power used internal, 6 of our 8 volts used internally
i = 1 makes more sense
then 2 volts lost internal and 6 of our 8 volts powers our load outside.
Well, let's see if we can clown around and find a solution to your question! To determine the current flowing through the circuit, we can use a little math and humor.
First, we need to find the total resistance in the circuit by adding the internal resistance of the battery to the external resistance. But remember, resistance is futile! Anyway, given that the internal resistance is 2 ohms, we'll need to know the external resistance.
Next, let's focus on power. Power is equal to the product of current and voltage. In this case, the power drawn by the external circuit is 6W. So, if we can find the current, we'll be one step closer to victory!
To calculate current, we can use the equation:
Power (P) = Current (I) squared times Resistance (R)
Now, let's rearrange the equation to solve for current:
I = √(P / R)
Plug in the power (6W) and the total resistance (internal resistance + external resistance) into the formula, and you'll have a possible current. Keep in mind that this is just one approach, but it's no joke - it should help you find the answer!
Good luck with your circuit calculations, and remember to have fun along the way!
To find the current in the circuit, you can apply Ohm's Law which states that the current (I) flowing through a circuit is equal to the voltage (V) across the circuit divided by the total resistance (R). In this case, the total resistance is the sum of the external resistance and the internal resistance of the battery.
First, let's determine the external resistance. We know that power (P) is equal to the current (I) multiplied by the voltage (V). So, in this case, the power is 6W and the voltage is 8V. We can use these values to find the current flowing in the circuit.
Power (P) = Current (I) * Voltage (V)
6W = I * 8V
Now, let's find the total resistance (R). The total resistance (R) is the sum of the external resistance and the internal resistance of the battery. In this case, the internal resistance is given as 2 ohms.
Total Resistance (R) = External Resistance + Internal Resistance
R = ? + 2Ω
Now, substitute the values of power (P) and voltage (V) into the equation and solve for the current (I).
6W = I * 8V
I = 6W / 8V
Once you have the value of current (I), you can substitute it into the equation for total resistance (R) to find the external resistance.
R = I - 2Ω
This will give you a possible current in the circuit.
To find the possible current in the circuit, you can use the formula for power in an electric circuit:
Power = (Current)^2 * Resistance
First, let's calculate the total resistance in the circuit. The total resistance is comprised of the internal resistance of the battery (2 ohms) and the resistance of the external circuit. However, we don't have the value for the external resistance, so we'll need to find it using Ohm's Law.
Ohm's Law states that the voltage across a component (V) is equal to the current (I) flowing through it multiplied by the resistance (R). In this case, the voltage across the external circuit is the voltage of the battery, which is 8V.
The formula can be rearranged to find the resistance:
Resistance = Voltage / Current
Since we have the voltage (8V) and the power (6W), we can find the current by rewriting the power formula:
Power = (Current)^2 * Resistance
Rearranging the formula gives:
Current = sqrt(Power / Resistance)
Now let's apply these steps to find the possible current in the circuit:
Step 1: Find the external resistance:
Resistance = Voltage / Current
Resistance = 8V / I (where I is the current)
Step 2: Calculate the current using power formula:
Current = sqrt(Power / Resistance)
Current = sqrt(6W / (2 ohms + calculated resistance))
Since the question asks for a possible current, you need to solve the equation for different values of the external resistance and calculate the resulting current.