If deflection in galvanometer in above circuit is zero then find value of R. Internal resistance of 12 V source is negligible. Will the galvanometer show some deflection if cold air is passed on 10 `k Omega` wire wound resistor ?

Explanation

Here, initially when deflection in the galvanometer is zero, potential difference across R is 2V. At this time if I amount of current passes through R then,
IR = 2 `rArr I = (2)/(R) " "` ....(1)
Also current passing through battery is,
` I = (12)/(R + 10000 ) " "` ... (2)
From equation (1) and (2),
`(2)/(R) = (12)/(R + 10000) `
`therefore 2 R + 20000 = 12 ` R
`therefore R = 2000 Omega " " ` .... (3)
When cold air is passed on the wire wound resistance, its resistance will decrease (because of decrease in temperature) which causes increase in current which then would increase potential difference across R and so some curent starts passing through galvanometer and so it will show some deflection.