Mobile signal strength is measured in decibel- milliwatts (dBm), with values ranging from (-50) dBm (excellent) to (-120) dBm (very poor), and can be checked using your phone's Field Test Mode or signal strength apps.

Signal strength S (in dBm) is calculated as :

S = 10 log P, where P is the signal power.

(i) Find the signal strength when P = $\dfrac{1}{10^6}$.

(ii) If signal power is reduced to $\dfrac{1}{10^{10}}$, how does S change?

Given,

S = 10 log P

(i) When P = $\dfrac{1}{10^6}$

P = 10^-6

S = 10 log (10^-6)

= 10 × (-6) log 10

= 10 × (-6) × 1

= -60 dBm.

Hence, signal strength = -60 dBm.

(ii) P = $\dfrac{1}{10^{10}}$ = 10^-10.

S = 10 log (10^-10)

= 10 × (-10) log 10

= 10 × (-10) × 1

= -100 dBM.

Hence, signal strength is reduced to -100 dBm.