A battery with an emf of 14.5 V and internal resistance of 0.83 Ω is connected across a load resistor R.

If the current in the circuit is 0.81 A, what is the value of R?

I=14.5/(R+.83)

solve for R

85A

To solve this problem, we can use Ohm's Law and the concept of EMF (electromotive force).

Ohm's Law states that the current through a conductor is equal to the voltage across the conductor divided by its resistance. Mathematically, it can be written as:
I = V / R

Where:
I is the current (in amperes)
V is the voltage (in volts)
R is the resistance (in ohms)

In this problem, we are given the current I (0.81 A) and the EMF of the battery (14.5 V). However, the battery also has an internal resistance (0.83 Ω), which we need to take into account.

The total voltage across the circuit can be calculated using the formula:
V_total = V - (I * R_internal)

Where:
V_total is the total voltage across the circuit
V is the EMF of the battery
R_internal is the internal resistance of the battery

Substituting the given values, we have:
V_total = 14.5 V - (0.81 A * 0.83 Ω)

Now, we can use Ohm's Law to find the value of the load resistor R:
R = V_total / I

Substituting the calculated value of V_total and the given value of I, we have:
R = (14.5 V - (0.81 A * 0.83 Ω)) / 0.81 A

Evaluating this expression will give us the value of the load resistor R.