Question

two resistors of resistences5ohm &10ohm are to be connected toa battery of 6v so as to obtain(1)minimum current(2)maximum current... convert resistence in each case and strength of total current inboth cases

Answer 1

1) To get the minimum current you need to set up the circuit so that it has maximum resistance. Two resistors in series will always have more resistance than placing them in parallel. Placing them in series gives you a total resistance of:
\[R_{total}=5Ω+10Ω=15Ω\]Using ohms law you get a current of:
\[I=\frac{V}{R}=\frac{6V}{15Ω}=0.4A\]
2) To get the maximum current you need to set up the circuit so that it has minimum resistance. Two resistors in parallel will always have less resistance than placing them in series. Placing them in parallel gives you a total resistance of:
\[R_{total}=\frac{R_1R_2}{R_1+R_2}=\frac{5Ω∗10Ω}{5Ω+10Ω}=3.33Ω\]Using ohms law you get a current of:
\[I=\frac{V}{R}=\frac{6V}{3.333Ω}=1.8A\]