A battery of e.m.f. 6.0 V, and internal resistance 1.0 ohms is connected to a resistor and drives a current of 125 mA through it. What is the resistance of the resistor?
Thank you!!
When they ask for the resistor, do they mean the internal + external or just the external since they already give you the internal? One of my answer options is 47 ohms and the other is 48 ohms so I’m not sure which to go with.
To find the resistance of the resistor, we can use Ohm's Law, which states that the voltage across a resistor is equal to the current flowing through it multiplied by its resistance.
The voltage across the resistor can be found by subtracting the voltage drop across the internal resistance from the battery's electromotive force (e.m.f). In this case, the voltage drop across the internal resistance is equal to the current flowing through it multiplied by its resistance. The e.m.f of the battery is given as 6.0 V, and the internal resistance is given as 1.0 ohms.
Let's calculate the voltage drop across the internal resistance first:
Voltage drop = Current * Resistance
Voltage drop = (125 mA) * (1.0 ohms)
Since the current is given in milliamperes, it is necessary to convert it to amperes:
125 mA = 125 * 10^(-3) A
Substituting the values into the equation:
Voltage drop = (125 * 10^(-3) A) * (1.0 ohms)
Voltage drop = 0.125 V * 1.0 ohms
Voltage drop = 0.125 V
Now, we can calculate the voltage across the resistor:
Voltage across the resistor = e.m.f - voltage drop
Voltage across the resistor = 6.0 V - 0.125 V
Voltage across the resistor = 5.875 V
Finally, we can use Ohm's Law to find the resistance:
Resistance = Voltage across the resistor / Current
Resistance = 5.875 V / (125 * 10^(-3) A)
Calculating the final value gives:
Resistance = 46.875 ohms
Therefore, the resistance of the resistor is approximately 46.875 ohms.
To find the resistance of the resistor, you can use Ohm's Law. Ohm's Law states that the current (I) flowing through a conductor is directly proportional to the voltage (V) applied across it, and inversely proportional to the resistance (R) of the conductor. Mathematically, it can be expressed as:
V = I * R
In this scenario, the e.m.f. of the battery is given as 6.0 V, and the current flowing through the circuit is 125 mA (0.125 A). The internal resistance of the battery is 1.0 ohms.
So, we can rearrange Ohm's Law to solve for resistance:
R = V / I
Let's plug in the given values into the formula:
R = 6.0 V / 0.125 A
Now, divide 6.0 by 0.125:
R = 48.0 ohms
Therefore, the resistance of the resistor connected to the battery is 48.0 ohms.