Question

calculate the value of x.​

Answer 1

Answer:

The value of x is 12.4Ω.

Explanation:

First let us find the equivalent Resistance of the circuit.

The 12Ω,6Ω and 3Ω resistors are connected in parallel.

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$R_{p}$=$\frac{1}{R_{1} }$+$\frac{1}{R_{2} }$+...   and $R_{s}$=$R_{1}$+$R_{2}$+...

Thus the equivalent of these three resistors will be

$R_{p}$=$\frac{1}{12} +\frac{1}{6} +\frac{1}{3}$

⇒$R_{p}$=$\frac{1+2+4}{12}$      (taking LCM)

⇒$R_{p}$=$\frac{7}{12}$Ω

Now the effective Resistance of the circuit will be

R=2+$R_{p}$+x

⇒R=2+$\frac{7}{12}$+x

⇒R=$\frac{24+7+12x}{12}$

⇒R=$\frac{31+12x}{12}$Ω

As we know

from OHM'S Law

V=IR

here, V=6V, I=0.4A  and R=$\frac{31+12x}{12}$Ω

Substituting the values

6=0.4×$\frac{31+12x}{12}$

⇒6×$\frac{12}{0.4}$=31+12x

⇒6×30=31+12x

⇒12x+31=180

⇒12x=180-31

⇒12x=149

⇒x=$\frac{149}{12}$

∴x=12.4Ω