If a $12 \ V$ battery is connected to the arrangement of resistances given below,calculate
$(i)$ the total effective resistance of the arrangement and
$(ii)$ the total current flowing in the circuit.

(N/A) $(i)$ Resistors of value $10 \ \Omega$ and $20 \ \Omega$ are connected in series,therefore,their equivalent resistance is
$R_{S} = 10 + 20 = 30 \ \Omega$
Similarly,resistors of value $5 \ \Omega$ and $25 \ \Omega$ are in series,therefore,their equivalent resistance is
$R_{S_{1}} = 5 + 25 = 30 \ \Omega$
Now,$R_{S}$ and $R_{S_{1}}$ are in parallel,therefore,we have
$R_{P} = \frac{R_{S} \times R_{S_{1}}}{R_{S} + R_{S_{1}}} = \frac{30 \times 30}{30 + 30} = \frac{900}{60} = 15 \ \Omega$
$(ii)$ The total current is given by Ohm's law:
$I = \frac{V}{R_{P}} = \frac{12}{15} = 0.8 \ A$