A 12V battery with internal resistance 1 Ω is connected to a 23 Ω resistor. What is the pd across the 23 Ω resistor?
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THANK YOU!
the total resistance is 23+1 = 24Ω, so
23/24 * 12V = 11.5 V across the resistor, and 0.5 V in the battery.
Why did the battery go to therapy?
Because it had some serious internal resistance issues!
Now, let's get to your question. To find the potential difference (pd) across the 23 Ω resistor, we need to consider the total resistance in the circuit.
Given:
Battery voltage (V) = 12V
Internal resistance (r) = 1 Ω
External resistance (R) = 23 Ω
The total resistance (R_total) in the circuit is the sum of the internal and external resistances:
R_total = r + R
R_total = 1 Ω + 23 Ω
R_total = 24 Ω
Now, we can use Ohm's Law to find the current (I) flowing through the circuit:
I = V / R_total
I = 12V / 24 Ω
I = 0.5 A
Finally, we can calculate the potential difference across the 23 Ω resistor using Ohm's Law:
V_resistor = I * R
V_resistor = 0.5 A * 23 Ω
V_resistor = 11.5 V
So, the pd across the 23 Ω resistor is 11.5 V.
Hope this electrifying explanation brightened your day!
To find the potential difference (pd) across the 23 Ω resistor, we need to apply Ohm's law.
Ohm's law states that the pd across a resistor is equal to the current passing through the resistor multiplied by the resistance.
First, let's calculate the current passing through the circuit.
We can use Ohm's law again, which states that the current (I) is equal to the voltage (V) divided by the total resistance (R).
The total resistance in this circuit is the sum of the internal resistance of the battery (1 Ω) and the resistance of the 23 Ω resistor.
R_total = R_internal + R_resistor
R_total = 1 Ω + 23 Ω
R_total = 24 Ω
Now we can calculate the current passing through the circuit:
I = V / R_total
I = 12V / 24 Ω
I = 0.5 A
Now that we have the current, we can find the pd across the 23 Ω resistor:
pd = I * R_resistor
pd = 0.5 A * 23 Ω
pd = 11.5 V
Therefore, the potential difference across the 23 Ω resistor is 11.5 volts.
To find the potential difference (pd) across the 23 Ω resistor, we can use Ohm's Law, which states that the potential difference is equal to the current flowing through the resistor multiplied by its resistance.
First, we need to calculate the current flowing through the circuit. We can use the formula for calculating current in a circuit with a single resistor:
I = V / R
where I is the current, V is the voltage, and R is the resistance.
In this case, the voltage is the one supplied by the 12V battery. However, since the battery has an internal resistance of 1 Ω, the actual voltage across the circuit will be slightly less than 12V. We can calculate the effective voltage using the formula:
V_effective = V - I_internal × R_internal
where I_internal is the current flowing through the internal resistance and R_internal is the value of the internal resistance.
Substituting the given values, we have:
V_effective = 12V - I_internal × 1Ω
Next, we can calculate the current flowing through the circuit using Ohm's Law:
I = V_effective / (R_internal + R_resistor)
where R_resistor is the resistance of the 23 Ω resistor.
Substituting the given values, we have:
I = V_effective / (1Ω + 23Ω)
Now we can substitute this current value into the formula for potential difference:
pd = I × R_resistor
Substituting the given values, we have:
pd = I × 23Ω
Now we can solve for the pd:
1. Calculate the effective voltage:
V_effective = 12V - I_internal × 1Ω
2. Calculate the current flowing through the circuit:
I = V_effective / (1Ω + 23Ω)
3. Calculate the pd across the 23 Ω resistor:
pd = I × 23Ω
By following these steps, you should be able to find the pd across the 23 Ω resistor.