A circuit consists of a 10 ohm resistor in series with 3 identical batteries each with an emf = 1.0V and internal resistance of 5 ohms. a) find potential difference between the terminals b) potential difference across the 10 ohm resistor c) power dissipated in resistor
Thank you!
To find the potential difference between the terminals of the circuit, you need to calculate the total emf (electromotive force) of the batteries minus the total internal resistance.
To calculate the total emf, you simply add up the emfs of all the batteries in the circuit. In this case, you have 3 identical batteries, each with an emf of 1.0V, so the total emf would be:
Total emf = 3 * 1.0V = 3.0V
To calculate the total internal resistance, you also add up the internal resistances of all the batteries in the circuit. In this case, you have 3 identical batteries, each with an internal resistance of 5 ohms, so the total internal resistance would be:
Total internal resistance = 3 * 5 ohms = 15 ohms
Now, you can calculate the potential difference between the terminals of the circuit using Ohm's Law, which states:
Potential difference (V) = Current (I) * Resistance (R)
In this case, the resistance is the sum of the resistance of the batteries (15 ohms) plus the resistance of the 10 ohm resistor (which is in series with the batteries). So the resistance would be:
Resistance = 15 ohms + 10 ohms = 25 ohms
Now, we need to find the current flowing through the circuit. To do this, we can use Ohm's Law again:
Current (I) = Potential difference (V) / Resistance (R)
In this case, the potential difference is the total emf of the batteries (3.0V), so we have:
Current (I) = 3.0V / 25 ohms = 0.12 A
Finally, to find the potential difference between the terminals of the circuit, we can multiply the current by the total resistance:
Potential difference = Current * Resistance = 0.12 A * 25 ohms = 3.0V
So, the potential difference between the terminals of the circuit is 3.0V.
To find the potential difference across the 10 ohm resistor, you can use Ohm's Law again:
Potential difference (V) = Current (I) * Resistance (R)
In this case, the current is the same as we found earlier (0.12A), and the resistance is the value of the resistor (10 ohms). So, we have:
Potential difference = 0.12 A * 10 ohms = 1.2V
So, the potential difference across the 10 ohm resistor is 1.2V.
To calculate the power dissipated in the resistor, you can use the formula:
Power (P) = Current (I) * Potential difference (V)
In this case, the current is the same as we found earlier (0.12A), and the potential difference is the value we just calculated for the resistor (1.2V). So, we have:
Power = 0.12 A * 1.2V = 0.144W
So, the power dissipated in the resistor is 0.144W.
total resistance=10+3*5=25 ohms
current= 3v/25ohm=3/25 amp
a) 3v-ir=3-3/15*25=3-5/3 volt
b) v=ir=3/25*10=6/5 volt
c. Power=i^2 r