Question

The voltage across the $10\Omega$ resistor in the given circuit is $x$volt.

The value of $x$ to the nearest integer is_________.

Answer 1

Step 1: Given data,

$R_1=50\Omega$

$R_2=20\Omega$

$R_3$=$10\Omega$

$V=170V$

Step 2. Formula used,

For parallel resistance,

Equivalent resistance, $R_{eq1}=\frac{R_1\times R_2}{R_1+R_2}$

$R_1$ is the $50\Omega$resistance

$R_2$ is the $20\Omega$resistance

For series resistance,

Equivalent resistance, $R_{eq2}=R_3+R_{eq1}$

$R_3$ is the $10\Omega$resistance

$V=IR$, $V$ is the potential, $I$ is the current

Step 3. Calculating the equivalent resistance:-

To calculate the equivalent resistance in parallel as

$R_{eq1}=\frac{R_1\times R_2}{R_1+R_2}$

$R_{eq1}=\frac{50\times 20}{50+20}$

$R_{eq1}=\frac{1000}{70}\Omega$

$R_{eq1}=\frac{100}{7}\Omega$

For series,

$$\begin{gathered} R_{eq2}=R_3+R_{eq1} \\ {R}_{eq2}=10+\frac{100}{7} \\ {R}_{eq2}=\frac{170}{7}\Omega \end{gathered}$$

Step 4. Calculating the current,

$I=\frac{V}{R_{eq2}}=\frac{170}{{\displaystyle \frac{170}{7}}}=7A$

Step 5. Calculating the voltage,

$7A$ current will flow through $10\Omega$ the resistor,

Potential across$10\Omega$,

$V_{10}=7\times 10$

$V_{10}=70V$

Hence, the value of $x$ to the nearest integer is $70V$