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.
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.
$(i)$ 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
$R _{ P }=\frac{ R _{ S } R _{ S _{1}}}{ R _{ S }+ R _{ S _{1}}}=\frac{30 \times 30}{30+30}=\frac{900}{60}$
$=15 \Omega$
$(ii)$ The total current is given by
$I=\frac{V}{R_{p}}=\frac{12}{15}=0.8 A$
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