Two resistors are connected in series as shown in the diagram. $(i)$ What is the current through the $5\, ohm$ resistor ? $(ii)$ What is the current through $R$ ? $(iii)$ What is the value of $R$ ? and $(i v)$ What is the value of $V$ ?
Two resistors are connected in series as shown in the diagram. $(i)$ What is the current through the $5\, ohm$ resistor ? $(ii)$ What is the current through $R$ ? $(iii)$ What is the value of $R$ ? and $(i v)$ What is the value of $V$ ?
Given
Potential difference across $5\, ohm$ resistor $=10 V$
Potential difference across $R$ ohm resistor $=6 V$ Value of resistance $R_{1}=5$ ohm, $I=?, R=?$ and $V=?$ By Ohm's law, the current through resistor of $5\, ohm$ is
$(i)$ $\quad I=\frac{V}{R}=\frac{10}{5}=2 A$
Since the two resistors are connected in series, therefore, the current through resistor $R$ is also $2$ ampere.
Therefore, value of $R$ can be obtained as follows
$(ii)$ $\quad R =\frac{ V }{ I }=\frac{6}{2}=3 ohm$
$(iii)$ Since the resistors are in series, therefore, net resistance of the circuit is
$R = R _{1}+ R _{2}=5+3=8 \Omega$
Hence, by the expression $V = IR ,$ we have
$V =2 \times 8=16 V$
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