A battery has an emf of 15.0V and internal resistance of 0.0700 ohms. Its terminals are connected to a load resistance of 5.00 ohms. Find the current in circuit and terminal voltage of the battery.
Question
A battery has an emf of 15.0V and internal resistance of 0.0700 ohms. Its terminals are connected to a load resistance of 5.00 ohms. Find the current in circuit and terminal voltage of the battery.
Solution
To solve this problem, we will use Ohm's law (V = IR) and the formula for total resistance in a series circuit (R_total = R_internal + R_load).
Step 1: Calculate the total resistance in the circuit. The total resistance (R_total) is the sum of the internal resistance of the battery (R_internal) and the load resistance (R_load).
R_total = R_internal + R_load R_total = 0.0700 ohms + 5.00 ohms = 5.07 ohms
Step 2: Calculate the current in the circuit. We can use Ohm's law to find the current (I). The emf (electromotive force) of the battery is equivalent to the voltage (V) in this formula.
I = V / R_total I = 15.0V / 5.07 ohms = 2.96 A
So, the current in the circuit is 2.96 Amperes.
Step 3: Calculate the terminal voltage of the battery. The terminal voltage (V_terminal) is the emf of the battery minus the voltage drop across the internal resistance, which can be calculated using Ohm's law (V = IR).
V_drop = I * R_internal V_drop = 2.96 A * 0.0700 ohms = 0.2072 V
V_terminal = emf - V_drop V_terminal = 15.0V - 0.2072V = 14.79V
So, the terminal voltage of the battery is 14.79 Volts.
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