Question

In FIGURE, what is the current supplied by the emf when

(a) the frequency is very small and

(b) the frequency is very large

Short answer

(a) The current supplied by the emf when frequency is very small is $0.10A$.

(b) The current supplied by the emf when frequency is very large is$0.20A$.

Step-by-step solution

Part (a) Step 1  : Given information

We are given that the values of

$\begin{array}{l}{R}_1=100\Omega \\ R_2=50\Omega \\ {\epsilon }_o=10V\end{array}$

And We have to find the current supplied by emf when the frequency is very small .

Part (a) Step 2: Explanation 

When the frequency is very small then the branch with inductor has a very small $X_L$

so

We get,localid="1649933493454" $$\begin{gathered} Z=R_1 \\ I=\frac{10}{100} \\ I\hspace{0.17em}=0.10A \end{gathered}$$

Hence the current is$0.10A$.

Part (b) Step 1: Given information

We are given that the values of $R_1=100\Omega$,$R_2=50\Omega$,localid="1650185571185" ${\epsilon }_o=10V$

and we have to find the current supplied by emf when the frequency is very large .

Part (b) Step 2: Explanation

When the frequency is very large then the branch with capacitor has a very small

so $Z=R_2$

$$\begin{gathered} I_{rms}=\frac{10}{50} \\ {I}_{rms}=0.20A \end{gathered}$$On solving we get,

Hence the current is $0.20A$.