What is the emf of a battery with a 0.15 Ω internal resistance if the battery delivers 1.5 A to an externally connected 5.0 Ω resistor?

To find the electromotive force (emf) of the battery, you need to use Ohm's Law and take into account the internal resistance of the battery.

Ohm's Law states that the voltage (V) across a resistor is equal to the current (I) passing through it multiplied by its resistance (R): V = I * R.

In this case, the external resistance is 5.0 Ω, and the current passing through it is 1.5 A. So, the voltage across the resistor is V = 1.5 A * 5.0 Ω = 7.5 V.

Now, you need to consider the internal resistance of the battery. The internal resistance affects the overall voltage across the battery terminals. The voltage output of the battery (emf) can be calculated by adding the voltage across the external resistor to the voltage drop due to the internal resistance.

To find the voltage drop due to the internal resistance, you need to use Ohm's Law again. The voltage drop across the internal resistance (V_drop_internal) can be calculated by multiplying the current passing through it (I) by the internal resistance (R_internal): V_drop_internal = I * R_internal.

In this case, the current passing through the internal resistance is also 1.5 A, and the internal resistance is 0.15 Ω. So, V_drop_internal = 1.5 A * 0.15 Ω = 0.225 V.

Now, you can calculate the emf of the battery by adding the voltage drop across the external resistor and the voltage drop due to the internal resistance: emf = V_external + V_drop_internal = 7.5 V + 0.225 V = 7.725 V.

Therefore, the emf of the battery is 7.725 V.

To find the emf of the battery, we can use Ohm's Law and Kirchhoff's Laws.

First, let's use Ohm's Law to find the potential difference across the 5.0 Ω resistor. We know that the current flowing through the resistor is 1.5 A, and the resistance is 5.0 Ω.

Using Ohm's Law (V = I * R), we can calculate the potential difference (V) across the resistor:
V = I * R
V = 1.5 A * 5.0 Ω
V = 7.5 V

Now, let's apply Kirchhoff's Voltage Law to the circuit. According to Kirchhoff's Law, the sum of the potential differences around any closed loop in a circuit must be zero.

In this case, we have two potential differences to consider: the potential difference across the 5.0 Ω resistor (which we just calculated as 7.5 V) and the potential difference across the internal resistance of the battery.

Let's label the potential difference across the internal resistance as V_internal.

According to Kirchhoff's Law, we can write the equation as:
V_internal - V = 0

Substituting the known values:
V_internal - 7.5 V = 0

Solving for V_internal:
V_internal = 7.5 V

Therefore, the emf (E) of the battery is equal to the potential difference across the internal resistance (V_internal), which is 7.5 V.