The resistance of a wire is given by \( R = \frac{\rho L}{A} \), where \( \rho \) is the resistivity, \( L \) is the length, and \( A \) is the cross-sectional area. Since the wires are made of the same metal and have the same length, the resistivity (\( \rho \)) and length (\( L \)) are constant. Therefore, the resistance is inversely proportional to the cross-sectional area.
Let \( R_1 \) be the resistance of the thicker wire and \( R_2 \) be the resistance of the thinner wire. The ratio of their cross-sectional areas is \( 4:1 \), so the ratio of their resistances is \( 1:4 \) (since resistance is inversely proportional to area).
Given that \( R_1 = 20\ \Omega \), we have:
\[ \frac{R_2}{R_1} = 4 \implies R_2 = 4R_1 = 4(20\ \Omega) = 80\ \Omega \]
When resistors are connected in series, their resistances add up:
\[ R_\text{total} = R_1 + R_2 = 20\ \Omega + 80\ \Omega = 100\ \Omega \]
The total resistance of the combination is \( 100\ \Omega \).
प्रादेशिक स्तर पर आयोजित होने वाली 100 मीटर की बाधा दौड़ में आपके मित्र को प्रथम स्थान मिला है। उसे बधाई देते हुए लगभग 40 शब्दों में एक संदेश लिखिए।
‘मेघला के आकार वाली पर्वत श्रृंखला ने पृथ्वी को चारों तरफ से घेर रखा है।’ – रेखांकित पदों की जगह उपयुक्त समस्तपद प्रस्तुत कीजिए तथा समास का नाम भी लिखिए।