What external resistance is the galvanic cell with an internal resistance of 0.2 Ohm

What external resistance is the galvanic cell with an internal resistance of 0.2 Ohm closed to if the voltage across its terminals is 1.4V and the EMF is 1.6V?

We start the solution with a short note given.

We know the internal resistance of 0.2 Ohm of the circuit, as well as the voltage at its terminals of 1.4 V and EMF of 1.6 V.

r = 0.2 ohm;

U = 1.4 B;

EMF = E = 1.6 B.

Find: R -?

Solution:

To calculate the current strength, we apply the formula:

I = E / (R + r);

and the formula:

I = U / R;

We equate the formulas and get the expression:

U / R = E / (R + r);

We apply the main property of proportion and we get equality:

R * E = U * (R + r);

Ur + UR = RE;

R (U – E) = -Ur;

R = Ur / (E – U);

Substitute the values:

R = (1.4 * 0.2) / (1.6 – 1.4) = 0.28 / 0.2 = 1.4 Ohm.