Two identical resistors of resistance R are conceded in series with a battery of potential difference V for time 't'.The resistor are connected in parallel.Compare the heat produced in 2 cases

Open in App

Solution

$D e a r S t u d e n t, F o r s e r i e s c o n n e c t i o n, t o t a l r e s i s i \tan c e i s, R_{t} = R + R = 2 R H e a t p r o d u c e d i s, H_{s} = \frac{V^{2}}{R_{t}} \times t = \frac{V^{2}}{2 R} \times t F o r p a r a l l e l c o n n e c t i o n, t o t a l r e s i s i \tan c e i s, R_{t} = \frac{R \times R}{R + R} = \frac{R^{2}}{2 R} = \frac{R}{2} H e a t p r o d u c e d i s, H_{p} = \frac{V^{2}}{R_{t}} \times t = \frac{V^{2}}{\frac{R}{2}} \times t = \frac{2 V^{2}}{R} \times t \frac{H_{p}}{H_{s}} = \frac{\frac{2 V^{2}}{R} \times t}{\frac{V^{2}}{2 R} \times t} = \frac{2 V^{2}}{R} \times \frac{2 R}{V^{2}} = \frac{4}{1} \Rightarrow H_{p} = 4 \times H_{s} H e a t p r o d u c e d i n p a r a l l e l c o n n e c t i o n = 4 \times H e a t p r o d u c e d i n s e r i e s c o n n e c t i o n R e g a r d s .$

Suggest Corrections

Similar questions

A torch bulb is rated 2.5V and 750mA. Two identical resistors, each of resistance 2 ohm , are connected in series and parallel to a battery of 12 V Calculate ratio of power consumed in two cases.

Q. Two resistors

400 Ω and 800 Ω

are connected in series across a

6 V

battery. The potential difference measured by a voltmeter of resistance

10 k Ω across 400 Ω

resistor is close to:

6 Ω

and

12 Ω

resistors are connected in parallel. This combination is connected to series with a

10 V

battery and

6 Ω

resistor. What is the potential difference between the terminals of the

12 Ω

resistors?

Two resistors $2 Ω$ and $5 Ω$ are connected in series with a $7 V$ battery. Find the potential difference across the $5 Ω$ resistor.

Join BYJU'S Learning Program