A voltmeter of internal resistance of 5000 Ω is connected across the poles of a battery of internal resistance 0.20 Ω. The voltmeter reads 1.4993 volts. What is the actual zero-current emf of the battery?
Would this formula be I = V/(r+R) = 1.4993/(5000+0.20)?
I (r+R) = V, where V is the zero-current emf. I is the current when the measurement is made. R is the voltmeter's internal (series) resistance. r is the battery's internal resistance.
The measured voltage is I R = V' = 1.4933
V = (V'/R)*(r+R) = 1.4933*(5000.2/5000)
= 1.4934
which is not much different.
Yes, the formula you mentioned, I = V/(r+R), can be used to find the current flowing through the circuit. However, to determine the actual zero-current emf of the battery, we need to use a slightly modified formula.
The formula to calculate the zero-current emf (E) of the battery is given by:
E = V + I * r
where V is the reading on the voltmeter, I is the current flowing through the circuit, and r is the internal resistance of the battery.
In this case, the current flowing through the circuit can be calculated using:
I = V/(r+R) = 1.4993/(5000+0.20)
So, once you find the current (I), you can substitute the given values of V, r, and R into the formula to calculate the zero-current emf (E) of the battery.
Yes, you are correct in using Ohm's Law to find the current flowing through the circuit. The formula I = V/(r+R) is the correct one to use, where I represents the current, V represents the voltage, r represents the internal resistance of the voltmeter, and R represents the internal resistance of the battery.
To find the actual zero-current electromotive force (emf) of the battery, we need to rearrange the formula. Since I = V/(r+R), we can rearrange it to V = I * (r+R).
Given that the internal resistance of the voltmeter (r) is 5000 Ω, the resistance of the battery (R) is 0.20 Ω, and the voltage (V) read on the voltmeter is 1.4993 volts, we can substitute these values into the formula to find the current:
I = V/(r+R)
I = 1.4993/(5000+0.20)
I ≈ 0.0002999 Amperes
Now that we have the value of current, we can substitute it back into the formula to find the actual zero-current emf of the battery:
V = I * (r+R)
V = 0.0002999 * (5000+0.20)
V ≈ 1.4995 volts
Therefore, the actual zero-current emf of the battery is approximately 1.4995 volts.