Question

Two coils of resistances, R₁ = 3 Ω and R₂ = 6 Ω, are connected in series to a battery of pd 12 V. Draw a circuit diagram and determine the total electrical energy supplied by the battery in 1 min.

Answer 1

Given Data:

Resistance of first coil (R₁) = 3 Ω

Resistance of second coil (R₂) = 6 Ω

Potential difference of the battery (V) = 12 V

Time interval (t) = 1 minute = 60 seconds

1. Calculate Total Equivalent Resistance (R_s):

Since the two coils are connected in a series combination:

R_s = R₁ + R₂

= 3 + 6

= 9 Ω

2. Calculate the Total Electrical Energy (E):

Using the electrical energy formula derived from Joule's Law of Heating:

\(E=\frac{V^{2}}{R_{s}}\times t\)

= `(12^2)/9 xx 60`

= `144/9 xx 60`

= 16 × 60

= 960 J

The total electrical energy supplied by the battery in 1 minute is 960 Joules.