In the figure shown above, a cell of negligible internal resistance and emf 22 V is connected to a network of resistors. If the power dissipated in the whole circuit is x 10 R , then the value of x is:

Step-by-step solution

The diamond network forms a Wheatstone bridge. Left arm ratio: 4R 8R = 1 2 , Right arm ratio: 2R 4R = 1 2 . Since ratios are equal, the bridge is balanced — no current flows through the horizontal branch ( R + R = 2R ), so it is removed. Remaining three parallel paths in the diamond: Left path: 4R + 8R = 12R Right path: 2R + 4R = 6R Vertical path: R + R = 2R Combining left and right paths in parallel: R_ outer = 12R 6R 12R + 6R = 72R^2 18R = 4R Combining with vertical path: R_ diamond = 4R 2R 4R + 2R = 8R^2 6R = 4