# What is the impedance of an ac RC parallel circuit if the resistance is 12 ohms and the capacitive reactance equals 5 ohms?

Jun 26, 2015

$1.78 - 4.26 i$

#### Explanation:

Parallel circuit:

If two resistances are in parallel,then we can replace the parallel combination of two resistances by a single equivalent resistance which is equals to the ratio of the product of those resistance values to the summation of those resistance values.

The single equivalent resistance shows the same affect as the parallel combination.

Here two resistances are :

1.the value of resistor(R),

2.the value of capacitive reactance(X_c).

$R = 12 o h m$

${X}_{c} = - 5 i$ohms [since it is imaginary term]

${Z}_{e} = \frac{R \times {X}_{c}}{R + {X}_{c}}$ [since it is parallel circuit]

${Z}_{e} = \frac{12 \times \left(- 5 i\right)}{12 - 5 i}$

${Z}_{e} = 1.775 - 4.26 i$[by using calci]

${Z}_{e} = \sqrt{{1.78}^{2} + {4.26}^{2}}$

${Z}_{e} = \sqrt{3.16 + 18.1476}$

${Z}_{e} = \sqrt{21.3}$

${Z}_{e} = 4.61 o h m$

Which is magnitude of impedance.