Power Dissipation in a Resistor: How Does Resistance Affect Energy Loss?

[Janiceleong26]

Homework Statement

Homework Equations

P=V²/R
P=I²R
V=IR

The Attempt at a Solution

As the resistance of R increases, the potential difference across R increases, so the power dissipated in R increases too. But I can't seem to see how the power decreases afterwards. Is it because, as time passes, the e.m.f of the battery dies out eventually?

 

[gneill]

Power is a product of current and potential difference: P = IV. What happens to the potential and current as the external resistance gets very large? Can the potential across R increase indefinitely?

 

[Janiceleong26]

Power is a product of current and potential difference: P = IV. What happens to the potential and current as the external resistance gets very large? Can the potential across R increase indefinitely?

The current becomes very small and the potential gets larger. Hmm I'm confused on which quantity to look at to determine the power.. Because if current becomes too small, then according to P=IV, power will then decrease. But as resistance increase, potential difference increases too, and again according to P=IV , power will then increase..

 

[gneill]

The current becomes very small and the potential gets larger. Hmm I'm confused on which quantity to look at to determine the power.. Because if current becomes too small, then according to P=IV, power will then decrease. But as resistance increase, potential difference increases too, and again according to P=IV , power will then increase..

Yes, you need to consider both quantities if you want to make a choice by logical deduction. Consider V and I when R is at the extremes of its values, say 0 Ω and ∞ Ω.

Alternatively, you can analyze the circuit and write an expression for the power as a function of R, then you can examine the curve mathematically.

 

[Janiceleong26]

Yes, you need to consider both quantities if you want to make a choice by logical deduction. Consider V and I when R is at the extremes of its values, say 0 Ω and ∞ Ω.

Alternatively, you can analyze the circuit and write an expression for the power as a function of R, then you can examine the curve mathematically.

I see.. So if R -> ∞ Ω, power decreases, as current decreases right? Ok I got the picture, thanks !