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Electricity

Hot goIITian

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21 Mar 2008 18:46:22 IST

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417

Alternating Current doubt

None

Can some one provide me a way to find out the impedance of circuit where resistor and inductor are in parallel ? I mean have we got to use phasor algebra there?

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gokul subramanian

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21 Mar 2008 18:50:48 IST

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do u mean only L,R or is there capacitor too?

gokul subramanian

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21 Mar 2008 18:57:05 IST

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let current thru induc =il n current thru resistor =ir
now tot current i=il +ir
=> V/z =V/jwL + V/R
=>1/z =1/jwL + 1/R=1/R- j/wL as j^2=-1
|1/z| =sqrroot of {1/R^2 + (1/wL)^2}
so |z|= 1/sqrroot of {1/R^2 + (1/wL)^2}

suresan

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21 Mar 2008 19:01:40 IST

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If you want to use phaser diagrams in this case please try this. It might workout.
The potential difference across both inductor and resistor will be the same and take it as V and Draw the phaser to represent V along +ve x axis. The current thrrough the resistor will be in phase with the voltage V, therefore draw the phaser for current through the resistor Ir along +ve x axis. In inductor current IL followes the voltage V by pi/2 radians.Therfore draw the phaser for the current through the inductor along -Ve direction of Y axis. Please see if it worksout, if you would. I am curius. It is just an idea

gokul subramanian

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21 Mar 2008 19:02:57 IST

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sir,my soln,is it correct

Sushmi Chatterjee

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21 Mar 2008 19:05:47 IST

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No there is no capacitor

Just check this diagram

The question is :

The series and parallel circuits shown in the figure have the same impedance and the same power factor.If R = 3 omega and X = 4 omega, find the values of R1 and X1.Also find the impedance and power factor.

Answer given is R1 = 8.33 omega and X1 = 6.25 omega , however my answer did not match .I got R1 = something like 11.67 omega.Please someone find out the values.

Source : Arihant Electricity and Magnetism

shridhar ramachandran

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21 Mar 2008 22:13:39 IST

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i think the qsn is wrong..
if they have same power factor AND impedence, then they have to have same resistance also rite??

$Power factor = P = \frac R Z = \frac 3 5 = \frac {R_1}{Z_1}$

Also $Z_1 = Z$

$=> R = R_1$

Huh?

gokul subramanian

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21 Mar 2008 22:15:49 IST

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power factor =
cos@=R/Z
so yeah hash has a pt

n for a sum lik this y exactly was i asked to derive the formula n post it

arpan1

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21 Mar 2008 23:11:26 IST

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@ sushmi

i would advice u to work from the fundamentals

check whether the source is a.c. or d.c.
first thing to recall is that the voltage across the capacitor and resistor in parallel will be same

now equate the voltages ...

u may use KVL is necessary...

this is the general approach to such problems..

i hope this solves ur doubt (if any)

if not, then u can nudge me for complete solution

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