An 8.0 Ω resistor and a 4.0 Ω resistor are

connected in series with a battery. The potential difference across the 4.0 Ω resistor is
measured as 9 V.
Find the potential difference across the battery.

R1 = 8 Ohms.

R2 = 4 )hms.
V2 = 9 Volts.

I = V2/R2 = 9/4 = 2.25A
E = V1 + V2.
E = I*R1 + 9
E = 2.25*8 + 9 = 27 Volts.

To find the potential difference across the battery, we need to calculate the total resistance of the circuit first.

Since the resistors are connected in series, the total resistance (R_total) is the sum of their individual resistances.

R_total = R1 + R2

Given:
R1 = 8.0 Ω
R2 = 4.0 Ω

Substituting the values, we get:
R_total = 8.0 Ω + 4.0 Ω
R_total = 12.0 Ω

Now, we can use Ohm's Law to find the potential difference across the battery.

Ohm's Law states that the potential difference (V) across a resistor is equal to the current (I) flowing through it multiplied by its resistance (R).

V = I * R

In this case, the total resistance (R_total) is equal to the resistance of the circuit. So, we have:

V = I * R_total

To find the potential difference across the battery, we need to know the current flowing through the circuit. However, the current is not given in the question. Therefore, we cannot determine the potential difference across the battery with the available information.

To find the potential difference across the battery, we need to use Ohm's law and the concept of total resistance in a series circuit.

In a series circuit, the total resistance is the sum of the individual resistances. So, in this case, the total resistance (R_total) would be equal to the sum of the resistance of the 8.0 Ω resistor (R1) and the 4.0 Ω resistor (R2).

R_total = R1 + R2
R_total = 8.0 Ω + 4.0 Ω
R_total = 12.0 Ω

Now that we have the total resistance, we can use Ohm's law to calculate the potential difference across the battery (V_battery). Ohm's law states that the potential difference (V) across a resistor is equal to the product of the current (I) passing through it and the resistance (R) of that resistor.

V = I * R

Since the resistors are connected in series, the same current flows through both resistors. Therefore, the potential difference across the battery (V_battery) is equal to the current (I) multiplied by the total resistance (R_total).

V_battery = I * R_total

To find the current (I), we can use the potential difference across the 4.0 Ω resistor (V_4).

V_4 = I * R2

Rearranging this equation, we can solve for the current (I):

I = V_4 / R2
I = 9 V / 4.0 Ω
I = 2.25 A

Now we can substitute the value of current (I) into the expression for the potential difference across the battery (V_battery):

V_battery = I * R_total
V_battery = 2.25 A * 12.0 Ω
V_battery = 27.0 V

Therefore, the potential difference across the battery is 27.0 V.