Relationship between CPU Usage and Battery Usage

Question

I'm comparing the resource consumption of two Android Apps.

App A uses accelerometer

App B uses both accelerometer and gyroscope

After reading these sensors, these apps does some processing on the sensor values. Now I measured their CPU usage using dumpsys cpuinfo as well as top command.
In general, App B uses 3-4 times more CPU than App A. The actual numbers are as follows: These results for single CPU and my phone is using Dual-core 1.2 GHz Cortex-A9 CPU (Samsung Galaxy S2).

App A (Average CPU Usage: 5%)

APP B (Average CPU Usage = 20%)

Then I measured the percentage battery usage for these two apps. I kept the Android phone in Aeroplane mode and only one of these two apps were running at a a specific moment of time. After running them for one hour, I get the following results:

Remaining battery level after one hour of use:

Idle mode: 99%  

Running App A: 96%

Running App B: 93%

I was expecting the same ratio with these battery level as I observed with CPU Usage.
I also tested these apps on a smartwatch ( CPU: Quad-core 1.2 GHz Cortex-A7) and I observed even smaller difference between the battery use. The observed results for one hour use are as follows:

Remaining battery level after one hour of use:

Idle mode: 99%  

Running App A: 87%

Running App B: 85%

So my question: Why the ratio of CPU usage for these apps is not reflected in their remaining battery levels? Or Shouldn't the CPU Usage be linearly related to the battery use ?
Could the reason be that multiple cores are active at the same, that's why I observe small difference between the their battery levels?
PS: I use partial lock in these apps.

— utengr | Sources

Answer

Long story short, battery comsumption depends not only on CPU but also every other part of your device.

Full version. An SoC consists of CPU, GPU, modem, north bridge, south bridge and RAM (on a discrete semiconductor chip but packed together into the same shell) altogether. Also the battery powers not only the SoC but also sensors, screen (which is usually the most power-consuming part) and wireless connection antennae.

A CPU has its own algorithm to control it's power and performance, which is called a 'governor'. A radical CPU governor tends to provide better CPU performance at the cost of high battery consumption, whereas a gentle governor will try to reduce battery consumption, resulting in lower CPU performance. The same applies to GPU and other parts of the SoC.

The screen is often the most battery-consuming part of a device, and the most decisive factors of a screen's power are size, resolution, brightness and technology (LCD or OLED). Cheaper phones and watches use LCD screens while high-end ones use OLED screen, as OLED uses significantly less power than an LCD one of the same specifications.

A watch usually has significantly less battery capacity but not-so-little screen power, which will decrease the draining difference in its battery stats while the screen is on. Besides, the sensors used on the phone and the watch may not be exactly the same, causing various differences.

The bottom line, the battery cost is determined by all parts of a device rather than only CPU. If another part is draining too much battery, you can't find large differences even though the CPU's power is highly variable.

— iBug | Sources

Relationship between CPU Usage and Battery Usage

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