Question
The internal resistance of a $$2.1\,V$$ cell which gives a current of $$0.2\,A$$ through a resistance of $$10\,\Omega $$ is
A.
$$0.5\,\Omega $$
B.
$$0.8\,\Omega $$
C.
$$1.0\,\Omega $$
D.
$$0.2\,\Omega $$
Answer :
$$0.5\,\Omega $$
Solution :
Given : $$emf\,\varepsilon = 2.1\,V$$
$$I = 0.2\,A,R = 10\Omega $$
Internal resistance $$r = ?$$
From formula.
$$\eqalign{
& \varepsilon - Ir = V = IR \cr
& 2.1 - 0.2\,r = 0.2 \times 10 \cr
& 2.1 - 0.2\,r = 2\,\,{\text{or}}\,\,0.2\,r = 0.1 \cr
& \Rightarrow r = \frac{{0.1}}{{0.2}} = 0.5\,\Omega \cr} $$