Question

Two lamp ${}^{\prime }{A}^{\prime }$ ratio $100$ Watt $220V$ and ${}^{\prime }{B}^{\prime }$ rated at $60$ Watt $200V$ are connected in series to an electric main supply of $220V$. The ratio of heat produced in lamp ${}^{\prime }{A}^{\prime }$ and lamp ${}^{\prime }{B}^{\prime }$ would be $\left(SAT\right)$

• A. $3:5$
• B. $5:3$
• C. $4:5$
• D. $5:4$

Answer 1

The correct option is A $3:5$

Supply voltage, $V=220V$

Lamp A :-

Power , $P_A=100W$

Voltage, $V_A=220V$

Resistance, $R_A=\frac{V^2}{P_A}=\frac{{220}^2}{100}=484Ohm$

Lamp B:-

Power, $P_B=60W$

Voltage, $V_B=200V$

Resistance, $R_B=\frac{V^2}{P_B}=\frac{{220}^2}{60}=\frac{4840}{6}Ohm$

Ratio of heat produced , $\frac{H_A}{H_B}=\frac{I^2\ast R_A}{I^2\ast R_B}=\frac{484}{4840/6}=\frac{6}{10}=\frac{3}{5}$ (Current will be same as both are in series)

Hence ratio of heat produced in the lamps A and B is 3:5.

Option A