Question

A battery of $9\,volt$ is connected in series with resistors of $0.2$ ohms,$0.3$ ohms, $0.4$ ohms, $0.5$ ohms and $12$ ohms respectively. How much current would flow through a $12$ ohm resistor?

Answer 1

Hint:Here we will first see what ohm’s law is, what is the statement of ohm’s law and then by using the mathematical expression of ohm’s law we will solve the given problem.The relationship between electric current and potential difference is defined by Ohm's law.The voltage applied to the most conductors is proportional to the current flowing through them.

Formula used:
Ohm’s law:
$V=IR$
where $V$ is the voltage through the conductor, $I$ is the current flowing through the conductor and $R$ is the equivalent resistance in the circuit.

Complete step by step answer:
Georg Simon Ohm, a German physicist, was the first to experimentally prove Ohm's law.If all physical conditions and temperature remain constant, Ohm's law states that the voltage across a conductor is directly proportional to the current flowing through it.

According to Ohm’s law
$V=IR$
Therefore, $I=V/R$
where, $R$ is the equivalent resistance of 0.2 Ohm, 0.3 Ohm, 0.4Ohm, 0.5 Ohm and 12 Ohm resistances.
As given, we know that these are connected in series.Hence, the value of $R$will be given by the sum of resistances.
$R=R_1+R_2+R_3+R_4+R_5$
$\Rightarrow R=0.2+0.3+0.4+0.5+12=13.4$ Ohm
The potential difference, $V=9V$
$I=\dfrac{9}{13.4} \\
\therefore I=0.671\,A$
We know that when resistors are connected in series, the current is the equal in all the resistors.

Hence, current in $12\Omega $ resistor $=0.67A$.

Note:One must know how to differentiate between series and parallel connections.When the current gets divided in a circuit that connection should be treated as a parallel connection and when the voltage gets divided that connection should be treated as series connection; here as one can see the voltage gets divided so the connection is series.