A workshop needs 6900 W of real power from a 230 V supply…

Step 1. Power factor $1$. $I = \dfrac{P}{V\cos\phi} = \dfrac{6900\ \text{W}}{230\ \text{V} \times 1} = 30$ A. The heat is $I^2r = (30\ \text{A})^2 \times 0.50\ \Omega = 450$ W.

Step 2. Power factor $0.6$. $I = \dfrac{6900\ \text{W}}{230\ \text{V} \times 0.6} = 50$ A. The heat is $(50\ \text{A})^2 \times 0.50\ \Omega = 1250$ W.