Question

A hot plate of an electric oven connected to a `220 V` lines has two resistance coils `A and B`, each of `24 Omega` resistance, which may be used separately, in series or in parallel. What are the currents in the three cases ?

Answer 1

(i) Calculation of current when each coil is used separately
Here, Potential difference, `V = 220 V`
And, Resistance, `R = 24 Omega` (One coil only)
Now, Current, `I = (V)/(R)`
`I = (220)/(24)`
`I = 9.17 A` ....(1)
(ii) Calculation of current when the two coils are connected in series
When the two coils of `24 Omega` each are connected in series, then their combined resistance will be `24 Omega + 24 Omega = 48 Omega`
Here, Potential difference, `V = 220 V`
And, Resistance, `R = 48 Omega` ( Two coils in series)
Now, Current, `I = (V)/(R)`
`I = (220)/(48)`
`I = 4.58 A` ...(2)
(iii) Calculation of current when the two coils are connected in parallel
When the two coils of `24 Omega` each are connected in parallel, then their combined resistance will be `12 Omega`. This is because:
`(1)/(R) = (1)/(24) + (1)/(24) = (1+1)/(24) = (2)/(24) = (1)/(12)` So, `R = 12 Omega`
Here, Potential difference, `V = 220 V`
Resistance, `R = 12 Omega` (Two coils in parallel)
Now, Current, `I = (V)/(R)`
`I = (220)/(12)`
`I = 18.34 A`