Abattery can be modeled as a source of emf in series with both a resistance of 10 ω and an inductive reactance of 5 ω. for a maximum power delivered to the load, the load should have a resistance of rl = 10 ω, an inductive reactance of zero, and a capacitive reactance of 5 ω. with this load, is the circuit in resonance?

Yes circuit is in resonance

Explanation:

As we know that the circuit consist of a resistance of 10 ohm and an inductive reactance of 5 ohm

This circuit is connected to a load with having value of resistance of 10 ohm and capacitive reactance of 5 ohm

now they are all in series so as we know that capacitor and inductor is in opposite phase so here reactance of inductor is cancelled by the reactance of capacitor due to the opposite phase of them also they are same in magnitude

so we have

so the circuit is purely resistive and hence we can say that it must be in resonance

a and b sometimes have a positive value