# We know that power is current squared times resistance, and also voltage squared divided by resistance.P=(I^2)*Ri.e. P is directly proportional to R..................(1)P=(V^2)/Ri.e. P is inversely proportional to R................(2)This presents a contradiction.  Why does this contradiction occur and which among (1) and (2) is correct?I've been wondering about this for long and am confused.  Help will be greatly appreciated!  Thank you.

Grade:11

## 6 Answers

Jaya IITK
207 Points
12 years ago
Current in the circuit is not independent..
It depends on resistance.
So u cannot take I as independent quantity
Since on changing the resistance both i and P will change.
To find relationship u need to have constant before proportionality
like:
P is proportional to (contant* R)
So we have to take
P = V^2/R
Since V is constant in the circuit
and thus we can say
P is inversely proprtional to R^2
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Yogesh Singh
15 Points
12 years ago
P = I^2R is used when current flowing in every component of the circuit is constant. This is the case of series combination of the devices in the circuit. P = V^2/R is used when potential difference (V) across every component of the circuit is constant. This is the case of parallel combination of the devices in the circuit.
BHARAT GAURAV
29 Points
12 years ago

P=(I^2)*R

IF CURRRENT IS CONSTANT THEN POWER IS DIRECTLY PROPORTIONAL TO RESISTANCE

AS HAPPENS IN SERIES CONNECTION.SUPPOSE THREE RESISTANCE 2,3&5OHM ARE CONNECTED IN SERIES THEN POWER CONSUMPTION

ORDER IS 5ohm>3ohm>2ohm.THIS IS BECAUSE DUE TO CONSTANT CURRENT IN THREE RESISTANCES" POWER CONSUMED~RESSTANE"

#P=V^2/R

IF POTENTIAL DIFF. IS CONSTANT THEN POWER IS INVERSELY PROPORTIONAL TO RESISTANCE

AS HAPPENS IN PARALLEL COMBINATION OF RESISTANCES. LET THREE RESISTOR OF INDIV. RESISTANCES 2,3&5 ohm CONNECTED IN PARALLEL THEN THE ORDER OF POWER CONSUMPTION IS AS FOLLOW

2ohm>3ohm>5ohm

the above trend is because power varies inversly with resistance in parallel combination

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Satchit beena Varma
14 Points
12 years ago

Clear and concise.  Thank you!

harshita shokeen
8 Points
10 years ago
this relation actually depends on the constant value if the current throughout the circuit is constant( as in case of series combination), resistance is directly proportional to power that is P=I^2* R if the voltage is constant throughout the circuit (as in case of parallel combination), resistance is inversely proportional to power that is P=V^2/R
hemant
21 Points
8 years ago
Hello friend i am hemant

The formula P = V^2 / R says that "If you keep the volts constant ( and permit the current to alter as it will ) then the power is inversely proportional to the resistance."
The formula P = I^2 R says that "If you keep the current constant ( and in turn permit the volts to vary accordingly) then the power consumed is proportional to the resistance".

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